Subversive, liberating, violent, transgressive and revolutionary, surrealism was always more than a parade of melting watches and trains chuffing out of fireplaces. It was also more than a European phenomenon. For a movement that officially began in Paris in 1924, with the publication of the first Manifesto of Surrealism, its ideas travelled around the world remarkably quickly to Osaka and Bogotá, Mexico and Manila, to Cairo and to Greenwich Village. Co-produced by Tate Modern and the Metropolitan Museum in New York, Surrealism Beyond Borders is filled with unlikely conjunctions and unsettling objects, Freudian dreamworlds, nightmares and fantasies. So surreal, so predictable. Where this exhibition – and its enormous catalogue – differs from previous surveys is in showing how expansive, sprawling and diverse a movement surrealism was, and how, emerging in the aftermath of the first world war, its influence continued through the century, in art produced in postwar Japan and Korea, in the black power movement and the protests at the 1968 Chicago Democratic Convention, and in the May 1968 protests and strikes in France. With its substitutions, its impossible juxtapositions, collisions and surprises, surrealism is with us still. What began as an avant garde movement (how quaint the term now sounds) has now become ubiquitous. The compendious, fascinating catalogue takes us from the Bureau of Surrealist Research in Paris to Sufism and surrealism in Turkey, and from surrealism in Brazil to the Philippines. Along the way we meet jazz musicians and poets, Leon Trotsky and a Vodou priest, surrealism’s fellow-travellers and oddball loners, feminists and revolutionaries, visionaries and misogynists. Sean O’Hagan writes in the catalogue of “a multifarious, polyphonic surrealism … a shifting, transnational assemblage from its very origins”, which is exactly what this exhibition presents. The rooms are filled with individual and group projects, and unlikely meetings and juxtapositions that are almost surreal in themselves. Ted Joans, jazz trumpeter, poet, painter and black power activist said that “jazz is my religion and surrealism my point of view”. Joans knew everyone, and first met André Breton at a bus stop in Paris in 1960. Joans’s Long Distance, an “exquisite corpse” drawing, produced over 30 years and involving 132 participants on three continents in its creation, concertinas its way along a wall for over 30ft. Among its contributors were writers John Ashbery, Michel Leiris and William Burroughs, artists Dorothea Tanning, David Hammons, Bruce Conner and a host of others. Spidery, sexy, automatist, this rambling collective drawing in which each of the file-card sized folds, produced by a different contributor, is a spontaneous compound trace of a kind of group unconscious. For a while, Joans shared an apartment with Charlie Parker, and commemorated him in Bird Lives, a 1958 painted black silhouette, seen from behind, hunched over his alto sax. In a film, we see Jones with sax player Archie Shepp, performing with Tuareg musicians at a Pan-African cultural festival in 1969. Other films here include New Zealand experimental film-maker Len Lye’s 1929 hand-drawn animation using Oceanic abstract motifs (it looks as fresh as the day it was made) and the great Czech animator and film-maker Jan Švankmajer’s 1968 stop-motion and live action Byt, which follows a terrified man racketing around his small Prague flat, which seems to conspire against him in various violent and absurd ways. That year saw the Prague Spring, and its suppression by invading Soviet troops. Filled with objects and drawings, photographs, films and much besides, almost everywhere you look there are terrible and alarming paintings, biomorphs with bristly spiky bits, droopy testicular ovoids, monuments in spooky deserted piazzas, disassembled bodies, Enrico Baj’s monstrous Body Snatcher terrorising a kitsch Swiss landscape, Yves Tanguy’s unctuous, slithery hinterlands. Along the way more familiar works remind us of the wearily familiar surrealist canon – Salvador Dalí’s telephone with a lobster for a hand-piece and Magritte’s locomotive in the fireplace, Picasso’s Three Dancers (to my mind, barely a surrealist painting at all) and a smudgy Arshile Gorky painting, whose presence here feels redundant. Reduced to a black, draped unrecognisable presence, the British-born surrealist Leonora Carrington stands among draped furniture and beside a lit candle in a room in Mexico City in 1962, photographed by Hungarian artist Kati Horna. Horna also partly inspired her friend Remedios Varo’s autobiographical 1961 triptych which recalls Varo’s strict Catholic upbringing in Spain, the weaving of a mantle for the world by a group of female artisans, and a depiction of the artist leaving Spain for Mexico. The paintings (reunited for the first time in many years) have the feel of a feminist, medievalist fairytale. The shadow of a crucifix falls across a city square in which a gigantic woman’s head stares in two directions at once, in a painting by Philippine artist Hernando R Ocampo. Painted in 1939, Ocampo mixes Catholic symbolism with surrealist strangeness, while Haitian Hector Hyppolite, a third-generation Vodou priest and painter (who, for a long time, used chicken feathers for brushes), applies a rather different kind of syncretism, between Catholic and Vodou symbolism, in his paintings. In one, there are knives and axes, a sacred heart, playing cards and a figure wielding a sword. A different kind of violence is implied in Alberto Giacometti’s 1930-31 The Cage, which manages to be both a delicately crafted, lathed and carved wood construction and also an image of dismemberment. Japanese surrealist Koga Harue, whose 1929 The Sea includes a swimsuit-clad Gloria Swanson, a cut-away view of a submarine, an airship, shoals of tropical fish, squid and the odd passing gull. What fun this painting is. Using found printed images as source material, Koga repainted and amalgamated them into a vision of technological advancement and pleasure, painted with almost photorealist finesse. Although criticised in Japan at the time as failing to reflect the realities of modern society, Koga was doing precisely the opposite. If this was surrealism, it was also pop art before the term existed, in the same way that Joseph Cornell’s little boxes of movie star mementoes and highly personal trinkets straddle both surrealist and pop sensibilities. In Okanoue Toshiko’s 1953 photo-collage The Call, an elegant Japanese woman sits in a room, dwarfing her surroundings. She seems as disquieted as a Hitchcock heroine. Outside the room is a raging sea. Amid the waves, a wolf howls. I know how it felt. Full of discoveries, Surrealism Beyond Borders is a tremendous work of scholarship, bringing together so many artists, so many essayists, so many threads and tangents, but indigestible as an exhibition. We travel too far, too quickly, with too many borders to cross. Surrealism Beyond Borders is at Tate Modern, London, from 24 February to 29 August.