Cubism was a modernist art movement that developed in Paris in the first decades of the twentieth century, by a community of multinational artists. The painters Pablo Picasso and George Braques first created the style, which featured images built out of harsh geometric shapes and used representational images to create broken depictions made up of peculiar shapes. Other important cubists included Fernand Léger, Juan Gris, Robert Delaunay, Jean Metzinger, and Henri Le Fauconnier.

The Mexican painter Diego Rivera first started his artistic career in the 1910s in Paris as a conventional Cubist. On the urging of the Mexican ambassador to France, Rivera began painting murals back in Mexico, which were large, symbolic, and drew on Mexican history and culture. This made Rivera an internationally famous artist, and he was commissioned to paint murals across the world.

Like fellow Pop Artists Lichtenstein and Warhol, Jasper Johns used familiar symbols and images, but reshaped and transformed them to present them in new ways. Unlike his fellow Pop Artists, who preferred commercial and pop culture symbols, Johns largely used icons of Americana, most notably the American flag and maps of the United States. One of Johns' most well known paintings is of an American flag that is completely in white.

Frida Kahlo was a Mexican artist who took up painting after a horrific bus accident at the age of eighteen in 1925 and her marriage to the European-trained muralist Diego Rivera. Kahlo painted almost entirely self portraits, typically close ups of her own face, to which she added in the background indigenous native imagery, surrealist symbols, and references to her own troubled life. Her stormy marriage to Rivera was well known, and combined with her ill health contributed to a sense of loneliness and alienation in her work.

Nighthawks was painted in 1942 by Edward Hopper, who sought to capture the inherent loneliness and suffocation of the "new" urban society as well as the effects of wartime.

Dada was an art movement that grew out of abstract and modernist movements in the early twentieth century. One of the most famous dadaist artists was Marcel Duchamp, a frenchman who began his career in a cubist vein, but then sought to make art that was less "retinal," or simply pleasing to the eye. Duchamp's art work challenged the very notion of what was "art," as in his 1917 "Fountain," a urinal Duchamp placed in the middle of a gallery space and only attributed as "R Mutt."

The Spanish Juan Gris arrived in Paris in 1906 and helped develop the style known as Cubism with fellow young artists Georges Braque and Fernand Léger, and under the influence of Gris' fellow Spaniard, Pablo Picasso. Fittingly, one of Gris' signature cubist portraits is of Picasso himself, with a clear depiction of the painter that also features a cubist deconstruction of his clothing and surroundings.

Figure: Portrait of Pablo Picasso by Juan Gris (1912)

Cubism, the style employed by Juan Gris in the painting seen here, was part of the broader trend of modernism, which was concerned with technological innovation, new ways of thinking, and breaking with tradition. A style which took many of modernism's and cubism's precepts even further was the Italian movement known as Futurism. As much a political movement as an artistic one, Futurism embraced machine age technology, progress, and activity in a cross-artistic style heavily indebted to cubism's breakthroughs.

Figure: Portrait of Pablo Picasso by Juan Gris (1912)

Pop Art was a twentieth-century art movement defined by the way it repurposed and engaged with everyday, common forms of art, like advertisements and comic books. The other answer describes elements of cubism (viewing  three-dimensional shapes from different perspectives at once).

The Dada school developed during the last years of World War I. Duchamp acted as a major contributor to the Dada school, and his work Fountain was one of the movement's best-known and most controversial works of art.