Picasso fell in and out of love with the Russian ballet dancer Olga Khokhlova in one fierce decade. His portraits trace the collapse. When they meet in 1917, she is an exquisite dark-eyed beauty, en pointe and lithe as an Ingres drawing. Four years later, she has become a monument of neoclassical maternity. By 1927, Picasso has fallen for the teenage Marie-Thérèse Walter, although Olga – now a sharp-featured crag – is the last to know.  When she finds out, Picasso paints a post-cubist rant: Olga as a pinched polyhedron with a hyphen-slot mouth and ridiculous hat. Her shining eyes are now dumb black pennies.  These images, and more, appear on opposite walls of this show so viewers can look back and forth between them. What strikes are all the usual wonders – Picasso’s stupendous draughtsmanship and super-fertile mind, always inventing new pictorial ideas – but also his sheer volatility. He is sardonic, lustful, exuberant, passionate, satirical, furious. The mood swings from love and camaraderie through humour to outright aggression. This is not Picasso as we generally know him.  If all portraits are caricatures, then Picasso’s portraits of other people are simultaneously caricatures of himself  In fact, the show is a true liberation from art-historical constraints. Its curator, Elizabeth Cowling, urges us to view Picasso as an actual man rather than an avant garde deity. She has assembled nearly 80 portraits from every phase of his career – blue period drinkers, cubist flâneurs, opulent nudes, caricatures, late self-portraits – in a condensed retrospective that fills the entire ground floor of the National Portrait Gallery. Nor are these pseudo-portraits, like the Tate’s Weeping Woman, lacking any sense of individual presence. Each image has force of personality, no matter how remote from conventional likeness.  Picasso is compulsive, constantly redefining the portrait for every sitter. Marie-Thérèse is a lavender moon or a rhythm of interlocking ovals, holding her own bosomy beauty together; the dealer Daniel-Henry Kahnweiler splinters in a fractal proliferation of graphic signs. Picasso’s first partner, Fernande, is broken into wintry planes at the end of the affair, built up in loving smudges at the start.  The sneaky vagabond Bibi-la-Purée looks out from such an overhang of impasto he seems to be literally squinting through the paint. The cultural critic Gustave Coquiot, face an arsenical green leer, backed by a chorus line, is given a real theatre of a portrait. The photographer Lee Miller is yellow and red, crisscross features in all the wrong places, but the scintillating combination conveys her brisk intelligence, regular American teeth and tailored jacket.  Picasso runs all the way from refined likeness to pictogram, metaphor and monstrous lampoon, adapting the style to the sitter. He can draw like Raphael (as he once boasted) yet depict his infant daughter Maya like a plump Peppa Pig. And the crux is always drawing, as this show successfully demonstrates. Picasso the schoolboy cartoonist becomes the quickfire genius encapsulating character and likeness in tight kernels of truth.  Take his sketch of Stravinsky – a perfect lesson in draughtsmanship. Here is the composer’s taut mask, inscribed with exacting frown lines, the collar summarily defined by the tie, the glasses two quick arcs that the mind’s eye completes. All of Stravinsky’s acerbity and logicality, his disciplined but almost unthinkable vision, are transcribed in these knife-edge contours. The hair is so sparingly drawn you can count the marks – and what’s hair but a sheaf of lines?  This is Stravinsky distilled, but not mocked. Picasso would have been the greatest caricaturist who ever lived had his imagination stopped at wit. And yet his portraits are often comic. Two grisaille paintings in this show are like frames from some early cartoon. Marie-Thérèse poses nude, breasts a plump sofa, nipples and eyes rhyming like upholstery buttons. Nusch Éluard, a professional acrobat, resembles a particularly spiky Wilma Flintstone.  Picasso’s style here, in 1938, seems to prefigure the great Hanna-Barbera era. And not the least humour lies in the artist’s self-parody. Nusch’s eyes have swapped places on either side of her nose, cubism caricatured years later. Picasso darts restlessly back and forth between styles. A 1954 portrait of his second wife, Jacqueline, her face a white oval framed by a black scarf, conflates early blue period sentimentality with neoclassicism and hints of El Greco. Later, she has become an armour-plated warrior, one fish-eye trained upon the artist in the gloomy interior, the other on the green world through the window. She looks like a post-cubist Minoan.  The portrait is dark, claustrophobic, oppressive; its geometric forms are scored into the surface with the brush end. But even these marks remain suavely athletic. Picasso’s signature is in every line of his work, and every line communicates the sheer physical virtuosity of its making.  Jacqueline sat regularly for Picasso, though he also worked from photographs and memory. But what this show reveals is a more startling source for the portraits. Picasso’s paintings talk back and forth across the gallery (it never really feels as if he’s dead), calling each other into being. The coinages in one are ramified in another, shapes are echoed, riffs multiplied, reprised or distorted. Look from neoclassical Olga to polyhedron Olga and you see it is not just the woman but her painted portrait that’s mocked.  And Picasso also rounds on himself: filthy monkey, priapic octogenarian, bony death’s head with sightless eyes (what lies beyond?) Even the late brothel etchings – Rembrandt badly overexcited, Raphael making love, but not so passionately he has to put down his brushes – are self-satirical, exposing Picasso’s notoriously competitive streak. If all portraits are essentially caricatures, to paraphrase the artist, then Picasso’s portraits of other people are simultaneously caricatures of himself.  And that is the revelation of this enthralling show: it humanises Picasso, weaving the story of his life with that of his art in a most intimate way. And he himself saw it as a vast pictorial autobiography. Certainly the subject of his portraits is picture-making – the late takes on Velázquez are nothing less than portraits of pictures – as much as the human beings who came before him. But for all his superhuman genius, Picasso turns out to be just as mortal.  Philippe Parreno, French film-installationist extraordinaire, has transformed the Turbine Hall at Tate Modern into a subaqueous tank. Or perhaps it is an isle full of noises. Inflatable fish drift intermittently through the air, mesmerising the crowd at the door; screens descend from the heavens to audiences sprawled on carpets below. Lights shimmer, murmurs rise and fall through the air.  Nina Conti, onscreen, ponders the universe, uttering a stream of intergalactic thoughts about temporal dilation, semiconductors and the space-time continuum. Her face swims in a pool of limelight. Like Prospero, she seems to be dreaming, talking of tides, infinity and the strange creatures of the sea. One floats into view, eye like a mouth, tentacles clasping like hands. The squid is connected to us, yet utterly alien.  Parreno’s vision is appealingly unobtrusive: Conti quietly breathy, the ambient fluctuations controlled by the infinitely various motions of micro-organisms wired up to software. Slow-flowing, intriguing, this mysterious environment makes a shadow-play of spectators, as well as an audience, measuring their time in the gallery by changing all the time. It is art as perpetual evolution. You can’t step in the same sea twice.  • Picasso Portraits is at the National Portrait Gallery, London until 5 February 2017
Works from across the master’s life reveal a playful, self-mocking artist, while a sea of dreams engulfs the Turbine Hall