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.

It’s that time of year again. The National Portrait Gallery exhibits the finalists in the annual Taylor Wessing Portrait prize. The judges have seen 4,303 photographs from 1,842 photographers and now show us 57.

There’s something familiar about those dark, piercing eyes, but the impenetrable, mask-like countenance of Picasso’s Self-Portrait with Palette, 1906, is ultimately unknowable. In fact, the painting serves as something of a rebuke: we think we know Picasso so well, but we don’t. It’s a theme emphasised by the hang of this exhibition, and the bewildering range of styles and formats from Picasso’s early years results in a visual discord that underlines his chameleon-like tendencies.

This exhibition includes one of my images, so I hesitated when I was asked to write about it – but I only hesitated for a moment. I have learned that if you are reluctant to promote your own work other people are even more inclined in that direction, so you should seize any chance you get.

American photographer William Eggleston is famous for dedicating himself to colour photography at a time when it was still considered kitsch – acceptable for wedding and Christening photos, but not much else. The best known example of his embrace of colour is a 1973 photo of a red light bulb hanging from a red ceiling, a picture devoid of subject matter beyond redness and the associations it triggers.

The opening image of this new David Hockney exhibition – a sketchily painted portrait of a seated man, slumping heavily forward, his head buried in his hands – could be a portrait of Brexit despair.

The huge and gorgeous Titian, The Vendramin Family, c.1540-c.1560, displays a frieze of males of all ages, three or four generations – and an adorable lap dog held close by the youngest boy – in marvellously sumptuous costume. The painting is surrounded with portraits by an ardent admirer of Titian's, Anthony van Dyck, our interest in the Titian deepened by the fact that Van Dyck once owned it. It is but one of the stars of this fascinating sampling of the collecting habits of artists themselves.

A good half of the portraits in Russia and the Arts are of figures without whom any conception of 19th century European culture would be incomplete. A felicitous subtitle, “The Age of Tolstoy and Tchaikovsky”, provides a natural, even easy point of orientation for those approaching Russian culture, and with it the country’s history and character, without particular advance knowledge.

Once you’ve seen him, you can’t forget him. Taken in 1951, Paul Strand’s black and white portrait of a French teenager sears itself onto your retina. He stares unflinchingly back, and looking into his eyes, you feel almost scalded by his exceptional beauty and the piercing intensity of his gaze. With his chiselled features, Roman nose, curled lips and leonine shock of hair, he could be a classical Greek sculpture; and as though to affirm this association, his skin has the sheen of burnished bronze. 

Much is made of the mystery surrounding Giorgione, a painter of pivotal influence, about whom, paradoxically, we know almost nothing beyond the manner of his death. He died in a Venetian plague colony in 1510 aged about 33, and was as elusive in the 16th century as he is today, his paintings highly sought after but hard to come by, and by the time of his death already invested with mythic status.