North London’s much loved Estorick Collection is reopening its doors after a five-month spruce up. The Georgian listed building that houses a 120-piece collection of modern Italian art now boasts a new glass conservatory, opened out entrance hall and "daylight-enhanced" gallery spaces. It all bodes well, even if the reliance on a period of prolonged British sunshine to complete the effect feels a touch optimistic right now. Here’s hoping.

It’s hardly the lot of an art critic to be loved and admired, still less to speak to an audience that might reasonably be called “the public”. And how many will find their ideas still current 40 years on? All of these things can be said for John Berger, who has died aged 90, a man whose radical approach to looking at art was an absolute inspiration, and whose ideas were a solid presence in my childhood, woven into my early memories as surely as the pages of a photo album.

The Good American, a Texan no less, has landed at Tate Modern in style. This posthumous retrospective of the great Robert Rauschenberg includes a paint-bespattered, fully made-up bed hung vertically on the wall, and called – you guessed – Bed,1955 (pictured below right). A huge White Painting, 1951 – latex housepaint on seven panels, glossy and smooth – is joined by a huge, swirling, all-black painting, Untitled, c.1951, and an installation of various substances resembling bubbling mud, called Mud Muse, 1968-71.

Born in Rome and taught by her artist father, Artemisia Gentileschi (1593-1652) led a colourfully energetic life. As an adolescent she was raped by her father’s assistant  – an episode which unusually, then as now, actually came to public trial – but she nevertheless became a confident, resolute woman, and a successful artist. She was vitally ambitious, portraying herself as La Pittura in her Self-Portrait as the Allegory of Painting, c.1638-9, an image at the heart of this exhibition.

The chances are, you’ve only ever seen Flaming June in reproduction: since 1963 it has resided in the Museo de Arte de Ponce in Puerto Rico, an out-of-the-way location that reflects the universal disdain for Victorian art in the post-war period. When the painting disappeared and then resurfaced in a house on Battersea Rise it was rejected by every British museum imaginable, eventually being bought by the enterprising curator Luis A Ferré, to form part of what is now recognised as a world-class collection of Victorian art.

Cheekily bottom-like, their downy skin blushing enticingly, these must be the sexiest apricots ever painted. If you held out your hand, you might just be able to touch them, there in the foreground of what is thought to be Caravaggio’s earliest surviving painting. Echoing the skin tones of a boy absorbed in the act of peeling fruit, the light highlights his hands and his downcast eyes make us voyeurs in a scene of unexpected sensuality.

When the French painter Fabienne Verdier told me she’d been invited to explore the relationship between painting and music at the world-famous Juilliard School in New York, I knew straight away that this unusual residency should be documented.

Today we amuse ourselves with Facebook clips of talking cats, but in the 1850s they had stereographs, pairs of identical photographs that, viewed through special lenses, become suddenly and gloriously three-dimensional. Vistas open up as if by magic, the illusion of space all the more beguiling for its transience. The act of looking through a special pair of glasses is a little bit like peeping behind a curtain, the intimacy of the encounter adding a slightly voyeuristic frisson to all manner of subject matter from landscapes to mock-ups of popular paintings.

Visceral and vividly colouristic, Clare Woods' paintings are at once abstract and figurative, perpetuating traditional genres but simultaneously occupying a less easily defined area of artistic practice. She puts innocuous or ambiguous subject matter into tension with titles and forms that suggest dark undertones, while big, universal themes are treated with the immediacy of personal experience. Her work is notable for its luscious paintwork and yet she is not a painterly painter, her initial training as a sculptor continuing to inform and shape her work.

Here be two modestly scaled masterpieces from the 1760s by George Stubbs, highlights of a centuries-old tradition of painting the horses owned by the Dukes of Newcastle and their lateral descendants the Dukes of Portland (the Devonshires are also connected in a grand web of aristocratic marriages). Stubbs was commissioned by the third Duke of Portland (1738-1809), William Cavendish-Bentinck, indisputably one of the grandest in the land: a politician and a multi-billionaire in today’s terms.