Pablo Picasso is the presiding genius of 20th century art, the most influential artist in the modern period, lauded for his protean inventiveness, originality, individuality and overwhelming productivity. In 1934 poet Geoffrey Grigson declared that he was all the history of modern art, in 1942 the artist Jankel Adler observed that “Picasso, the greatest innovator of the twentieth century, has knocked on the door of every painter’s studio in the world”. Too true: his ghost is still present amongst art’s practioners and its audience.

The easiest mistake to make in appreciating George Condo would be to assume that his manic style reflects a manic creation or a manic practice. Some of Condo's paintings and drawings, with their childlike loops and gurning, disfigured faces, look like he made them in a fit of violence or some hysterical trance, but the real surprise of two new shows at the Hayward Gallery and at Sprüth Magers in Mayfair is the care and the calmness that lies behind them.

An artist as inventive and as protean as Picasso, and one who ceaselessly absorbed influences throughout his life, will inevitably present an ever-changing face to the world. Hence, we have an apparently inexhaustible supply of exhibitions devoted to him.

February is guitar month in New York City. Synchronicity rules at those two giants, the MoMA and the Met. At MoMA, Picasso: Guitars 1912-1914 shows his austere guitar paintings, collages and drawings - often using newspaper, wallpaper and sand - as well as constructions of guitars made of cardboard and one of sheet metal and wire. “What is it? Painting or sculpture?” asked snooty visitors to his Paris studio. “It’s nothing, it’s el guitare,” Picasso, who didn’t play an instrument, is said to have replied.

Last year gave us three giants of Post-Impressionism. The Royal Academy promised to unveil the real Van Gogh by showing us the man of letters; Tate Modern delivered a sumptuous survey of Gauguin; and a significantly smaller but nonetheless intelligent and illuminating display at the Courtauld Gallery homed in on just one series of paintings in Cézanne’s oeuvre - the ambitious, masterly and compositionally complex The Card Players.

Sergei Diaghilev was not short of self-belief. He appointed himself the man to introduce European modern art to Russia and then Russian modern art to Europe as the 20th century began, and in doing so he defined himself as the ultimate artistic director, as the remarkable, tentacular exhibition at the V&A Museum that opened yesterday shows. Reviewed elsewhere on theartsdesk, the exhibition's mounting has thrown up extraordinary inside dramas - the telltale paper found in the boning of a 1916 tutu, the unlikely discovery of a stellar bust in a junk shop, and the legendary artists' sweat that no cleaning can obliterate.

Sergei Diaghilev was not short of self-belief. He appointed himself the man to introduce European modern art to Russia and then Russian modern art to Europe as the 20th century began, and in doing so he defined himself as the ultimate artistic director, as the remarkable, tentacular exhibition at the V&A Museum that opened yesterday shows. Reviewed elsewhere on theartsdesk, the exhibition's mounting has thrown up extraordinary inside dramas - the telltale paper found in the boning of a 1916 tutu, the unlikely discovery of a stellar bust in a junk shop, and the legendary artists' sweat that no cleaning can obliterate.

This time, the hype was perhaps deserved: Christie's did have a claim to be putting on, last night, the sale of the century.

Picasso the genius, the sensualist, the womaniser, the priapic beast. This much we think we know of the great Spanish artist. But how about Picasso the political activist? Picasso the supporter of women’s causes? Picasso the… feminist? Oh, yes, that Picasso. In a landmark Liverpool exhibition focusing on the years 1944 to his death in 1973, and bringing together 150 works from around the globe, Picasso becomes all of these things.

The war was over, Picasso was finally free to leave the privations of Paris behind him and to spend more time in the South of France, marking a return to his Mediterranean heritage. The Gagosian Gallery’s exhibition, curated by Picasso’s distinguished biographer John Richardson and the artist’s grandson Bernard Ruiz-Picasso, focuses on those Mediterranean years, between 1945 to 1962, when the artist was moving easily between styles.