Lending its name to a major photography prize for the 12th year running, Deutsche Börse has joined the ranks of business organisations known to many for their involvement in the arts rather than what they actually do. Unlike Taylor Wessing or Man Booker, the clue is in the name: German Stock Exchange is reasonably self-explanatory, at least if you speak the language.

The Other Room, dating from the late 1930s, is the largest painting in Dulwich Picture Gallery's landmark retrospective, the first show to be dedicated to Vanessa Bell since a posthumous Arts Council show in 1964. In it, three women inhabit a space crowded with sofa and armchair, flowers and a vase, a comfortable interior and yet also oddly mysterious: their body language hints at complex relationships.

It may be a cliché to say that this is a “timely” exhibition, but America After the Fall invites irresistible parallels with Trump’s America of today.

Love is in the air. Today, men and women and boys and girls will be pondering how to say it with roses and cards and candlelit dinners: those three words that contain multitudes. As the old strip cartoon never quite got round to saying, love is... the human condition, which is why a good quantity of the culture we review on this site has to do with it. To help you get into the mood for romancing, we have asked our writers to identify something - anything - in the arts that embodies the L word. There are some obvious choices, some obscure ones, and a whole lot of omissions. So, in the comment box at the bottom of the page, please let us know what you would include in the list.

Casablanca (1942)

"Where I’m going, you can’t follow." Bogart-Bergman. Just for once, won’t Rick just let his heart hold sway? But no. Casablanca teaches us that the best cynics follow a higher order, their better natures. In that wonderful final moment, Bergman’s eyes and Bogart’s drawl create the perfect magnetic field. Gets me every time. Carole Woddis

"Some Enchanted Evening", South Pacific [1949]

As lush and emotionally expansive a song as the musical theatre knows, this breakout hit from Rodgers & Hammerstein’s tale of wartime romance builds to a pitch of such sustained ecstasy as to make immediate lovers of all who hear it. And leave it to Oscar Hammerstein II to come up with a lyric worth of Shakespeare in “fools give you reasons / wise men never try”.  I'll swoon to that. Matt Wolf

Brassaï: Lovers in a Café on the Place d'Italie, Paris (1932)

The Transylvanian photographer was the "eye of Paris", photographing everybody and everything from prostitutes to socialites, from Picasso to graffiti - and lovers. The delight of the couple, who look thoroughly experienced, is reflected in the café mirrors: flirtatious, tender, determined and accompanied by those essential accessories, wine, coffee, cigarettes, with the kiss just about to happen. Marina Vaizey

In a Lonely Place (1950)

Hadda Brooks is singing the blues "I Hadn't Anyone 'til You" in a Hollywood jazz bar. Languorously smoking at the opposite end of her grand piano, Dix Steele (Humphrey Bogart) and Laurel Gray (Gloria Grahame) can't stop appreciating each other – their lovemaking, which occurred perhaps an hour before, has left them in a satiated haze. When Dix lights a cigarette and pops it between Laurel's lips, then whispers something in her ear, she smiles naughtily. Their eyes indicate they are the only two people in the world, though the director Nicholas Ray pulls back the camera to show the room is full of lovers. It couldn't possibly last, for Grahame and Ray (whose marriage was collapsing), for Dix and Laurel, for any of us. But there, for a moment, is Intimacy Incarnate. Graham Fuller

Chet Baker: "My Funny Valentine" (1959)

If your love’s looks are laughable, there’s no better way to say so than Rodgers’ and Hart’s touching expression of quirky love. Miles Davis’ 1965 version is surely the most sophisticated, and there’s always Sinatra for the full treacle, but Chet Baker’s fragile, wispy, meandering voice captures the vulnerability perfectly. As a YouTuber comments beneath this video: “No technique. No vibrato. No range. Sketchy pitch. And absolutely beautiful.” Matthew Wright

The Bridges of Madison County (1995)

This is love as the road not taken. Clint Eastwood's film of the novel by Robert James Waller, about a sudden passion in the autumn of middle age, cast himself as a National Geographic photographer wandering into the life of Meryl Streep's Italian war bride in rural Iowa for four days of exquisite pleasure, then a lifetime of pain. Instead of diving out the car into the rain (see clip below), she does the decent thing and internalises his memory, and what could be more romantic than that? A Brief Encounter for the sexually incontinent Clinton era. Jasper Rees

Wayne County & the Electric Chairs: “Eddie & Sheena” (1978)

When cross-dressing eccentric Wayne County – later Jayne County – arrived in London from New York in 1977 to horn in on the punk scene, he immediately made a mark by naming his band The Electric Chairs. His first single was topped with the charming “F** Off”: refrain “If you don’t want to f*** me, f*** off”. Two releases on, in 1978, he had mellowed with “Eddie & Sheena”, the actually charming tale of the forbidden romance and marriage of teddy boy Eddie and punk rocker Sheena. Kieron Tyler

Constantin Brancusi: The Kiss (1916)

Brancusi carved his first version of The Kiss in 1907. It was a theme the Romanian-born sculptor returned to again and again, each time simplifying his depiction of the entwined lovers. Working briefly as Rodin’s assistant (though he soon left because “nothing grows under large trees”), Brancusi took the older artist’s naturalistic and erotically charged representation of the illicit lovers encountered in Dante’s Inferno to create a proto-Cubist, “primitivistic” masterpiece which is at once much sweeter and more innocent in tone and sentiment. Fisun Güner

Frederick Ashton: La Fille mal gardée (1960)

Ballet's most erotic moment - Lise, Widow Simone’s disobedient daughter, is locked into the house with the newly harvested corn-stacks and the menace of an unwanted marriage. She sadly mimes her dreams of true love and babies - when out of the cornstacks jumps her boyfriend, hidden among them. She’s horribly embarrassed. He gently kisses up one arm, then the other, more sexily. An orgiastic pas de deux is threatened... But Mother’s on the way back. Ismene Brown

Dirty Dancing (1987)

Yes, it's corny, but boy, is it sexy; two lovers meet across the social divide as holiday-camp dancer Johnny Castle (Patrick Swayze) teaches prissy Baby Houseman (Jennifer Grey) how to loosen up and dance. And that moment, at the very end of the film, when Johnny mouths the words “And I owe it all to you” as they dance to “(I've Had) The Time of My Life” - meltdown. Veronica Lee

 Ibrahim Ferrer: "Dos Gardenias"

“With these two gardenias I mean to say ‘I love you, I adore you”. “Dos Gardenias“ was a famous bolero written by Isolina Carrillo in the 1930s. Ibrahim Ferrer leant the song while playing with the Cuban bandleader Benny Moré, although in his earlier bands he only sang the fast numbers as his Santiago de Cuba accent from the east of the island was deemed inappropriate for romantic songs. What is poignant in the song is the transitoriness of the flowers, and indeed Ferrer was all too conscious of the fleeting, precious nature of love and life. Peter Culshaw

Much Ado About Nothing (1993)

There’s a particular scene in Kenneth Branagh’s 1993 adaptation of the Shakespeare comedy that wrenches the heart every time. Beatrice and Benedick, after a campaign of whispers and rumours orchestrated by their friends, finally admit they adore each other. “I love you with so much of my heart that none is left to protest,” declares Emma Thompson’s Beatrice to Branagh (at the time her real-life husband). Of course, this being Shakespeare, she then orders him to prove his love for her by killing his best friend... Caroline Crampton

Tchaikovsky/Bourne: Swan Lake Pas de deux (1875, 1995)

Poor old Pyotr Ilyich would have been amazed to see two men dancing his great Odette/Siegfried lovescene together with such tenderness – not a version likely to be seen in Russia today, though Matthew Bourne’s company did have an unhappy tour there. Bourne has often said that it’s not necessarily, or just, a gay romance: his prince’s longing for a masculine swan may just be reaching out for wildness and freedom from stifling convention. Everyone can understand that. But there’s a great love here in the taming of Adam Cooper’s dangerous beast, the coming-together as the solo cello finally joins the soaring violin (originally soprano and tenor in the operatic love duet Tchaikovsky adapted for his ballet). And the final moment where the swan carries the prince in his arms perhaps reminds us of Tom Daley’s odd coming-out speech when he said his lover made him feel "safe". David Nice

Dexter Gordon: "I Guess I'll Hang My Tears Out to Dry" (1962)

"S'il vous plaît, I would like to have the same thing he had." In the 1986 Tavernier film Round Midnight, Dexter Gordon in the character of Dale asked for a drink to make him fall over. Back in 1962, before leaving New York, he recorded this ballad of unrequited love for Blue Note, to make anyone lonely on Valentine's Day reach for their third Martini. Playing live, Dexter would have recited the words of the song before playing it. Tearfully, divinely, unforgettably. Sebastian Scotney

Continued overleaf

This must be the most depressing exhibition I have ever seen. Dedicated to the leaders of the Russian Revolution, the first room features official portraits by Isaak Brodsky of Lenin and Stalin plus drawings and models of Lenin’s vast mausoleum in Moscow’s Red Square.

The art dealers of today must be thanking their lucky stars that Philip Hook’s remarkable history of their trade stops where it does. For while it serves as an eminently useful if rather specialised reference book, it’s a history pushed along by a ferocious analysis of the art dealing fraternity, the general thrust of which is encapsulated in its no-nonsense title. From unsophisticated third party to plutocrats’ lifestyle consultant, the evolving persona of the art dealer has taken guises ranging from merchant, scholar, connoisseur and ultimately, "purveyor of fantasy".

As the UK prepares for a particularly severe cold snap, the opening of David Hockney’s major retrospective at Tate Britain brings a welcome burst of Los Angeles light and colour and Yorkshire wit and warmth. The exhibition, which opens in the lead-up to Hockney’s 80th birthday, will be deservedly popular – for many people, Hockney’s work is simply bright and beautiful. But the show also seeks to reveal the serious and consistent nature of Hockney’s interrogation of the meaning of picture-making, and his preoccupation with the joyous and rather subversive business of “looking”.

The curators have brought together Hockney’s youthful paintings from the 1960s (the earliest work is, in fact, an earnest self-portrait drawing of 1954 of the 17-year-old artist), with the iconic and intimate works of the intervening decades, right up to his brash (and less successful) recent paintings of 2016 – with the inclusion of two new pictures of the blue and red terrace of the artist’s present-day Hollywood home (overlooking lush gardens reminiscent of a Rousseau jungle) made especially for the exhibition. (Pictured below: Garden, 2015 © David Hockney. Photo: Richard Schmidt)As we make the journey through Hockney’s oeuvre – one that the artist has also clearly enjoyed revisiting – we move from his formative pictures as a student at the Royal College of Art in London, through to the breakthrough Los Angeles paintings – typified by A Bigger Splash (Hockney first moved to the Hollywood Hills in 1979) – to the first big room of the show: a stunning display that reunites Hockney’s celebrated series of large double portraits.

Despite the variety of media and subject matter, consistent themes emerge. Thus we find Hockney continually playing with the notion of flat, two-dimensional picture-making (revealing the inherent artifice, while trying to make the experience more "true"); critiquing the art fashions of the time (particularly abstract and conceptual art); showily improvising in the style of the artists who capture his interest (such as Dubuffet, Picasso and Munch); raunchily exploring homo-erotic relationships and his own sexuality (at a time when homosexuality was still illegal in the UK); and urging us to question, engage with and examine what we see. Sometimes his artistic response is annoyingly puerile, while at others Hockney can be genuinely profound in the way he expresses personal encounters with people and places.

Hockney sees himself as a humanist: his reaction to the dominance of abstract art was to paint "pictures with people in": and not just any people. His sitters are usually friends, family or lovers. He came out early – while at college – deciding to embrace his homosexuality in his art; these paintings reflect his life and boyish humour, from escapades with early boyfriends to graffiti in the gent’s toilets. By being so constantly self-referential, Hockney became drawn to ambiguity, both in terms of the way we see the world, and the way the world sees us. (Pictured above right: Ossie Wearing a Fairisle Sweater, 1970. Private collection, London © David Hockney)

The relationship between the artist and the viewer is also central to this preoccupation. As a result, his work sets out to challenge the one-point perspective enshrined by single-lens cameras and crystallised in the rigid perspective constructions of Renaissance painting. Most of Hockney’s work sets out to undermine this "paralysed Cyclops’s" view of the world, as he calls it – though it is perhaps as much a way of thinking as a way of seeing. For Hockney, however, the question seems to be why would anyone choose to present a world that is so full of variation and contradictions in such a prescriptive way, and not actively invite the viewer’s eyes to wander, to embrace peripheral and contradictory viewpoints, or to mischievously seize on a particular detail?

The expansive sun-flattened spaces of Los Angeles, with their geometric buildings, blue skies and swimming pools, may seem to have the stillness that one associates with a Renaissance landscape or abstract canvas – but the geometry is often disturbed by the human presence. One of the surprises of the exhibition is Hockney’s corresponding love of areas of surface detail (like the meticulously painted splash). In the double portraits – such as the 1968 portrait of Christopher Isherwood and his partner Don Bachardy – the great open spaces of LA are exchanged for a defined domestic space, delineated by the device of a shuttered window and the static charge between the two sitters.

Hockney’s interest in the human is intimately entwined with a feeling for the character of a place. The exhibition includes the winding hilly landscapes of his home in the Hollywood Hills (their fauvist colours capturing the dizzying journey to his Santa Monica studio) and the glowing landscapes of the Grand Canyon, followed by a contrasting room of Hockney’s expansive Yorkshire landscapes – selected from the many canvases that Hockney produced for his 2012 blockbuster at the Royal Academy. In these gentler Yorkshire landscapes – which are a celebration of the English seasons, especially the spring when the hedgerows burst with hawthorn blossoms – Hockney continues to play with the language of painting, using exaggerated perspectives and heightened colour, set off by areas of flat decoration depicting cow parsley and grass verges. (Pictured above left: Going Up Garrowby Hill, 2000. Private collection, Topanga, California © David Hockney)

This epic journey through the seasons continues in a room of four nine-screen video installations – capturing multiple viewpoints as we travel with the artist through space. The final rooms are part analogue, part digital – moving from a fine series of 25 charcoal drawings chronicling the arrival of the Yorkshire Spring (contrasted rather pointlessly with the terrace-scenes made on Hockney’s return to LA), to the same preoccupations played out through Hockney’s exploration of the digital: numerous images made on the iPhone and iPad. The inclusion of a number of animated iPad drawings, which show step-by-step how the artist makes his marks, layers his colour, fixes the objects in his eye, allows the viewer to share in the show business of Hockney’s recent transformations of the perceived world. There is, fortunately, better business than "show business" to be had in this show.

• David Hockney at Tate Britain until 29 May
• More visual arts reviews on theartsdesk

Overleaf: browse a gallery of Hockney paintings from the exhibition