Short answers, pulled from the story.
Abstract expressionism is an American art movement that emerged in the United States in the aftermath of World War II and gained mainstream acceptance in the 1950s. It was the first specifically American movement to achieve international influence.
The art critic Robert Coates first applied the term to American art in 1946, in a review of 18 Hans Hofmann paintings. The phrase itself is believed to have first appeared in Germany in 1919 in the magazine Der Sturm, and Alfred Barr used it in 1929 for works by Wassily Kandinsky.
Key figures in the New York School included Arshile Gorky, Jackson Pollock, Franz Kline, Mark Rothko, Willem de Kooning, Adolph Gottlieb, Clyfford Still, Robert Motherwell, and Lee Krasner. Sculptors such as David Smith and Louise Nevelson were also integral to the movement.
Action painting, a term Harold Rosenberg coined in 1952, emphasized the act of creation through gesture, brushstrokes, and dripped paint, as in the work of Jackson Pollock and Franz Kline. Color field painting, a term Clement Greenberg used, favored large, flat areas of color and effaced the individual mark, as in the work of Mark Rothko, Barnett Newman, and Clyfford Still.
After World War II, Paris was in upheaval and its climate for art was a disaster, while New York replaced it as the new center of the art world. Modernist artists, collectors, and dealers who fled Europe during the war settled in New York, and a new generation of American abstract expressionists came to dominate the world stage.
Since the mid-1970s it has been argued that the CIA saw the style in the early 1950s as representative of the United States as a haven of free thought and free markets, and as a challenge to socialist realist styles in communist nations. Frances Stonor Saunders detailed in The Cultural Cold War how the CIA promoted the painters through the Congress for Cultural Freedom from 1950 to 1967, though Michael Kimmelman later argued much of that account is false or decontextualized.
Abstract expressionism preceded and influenced Tachisme, Color Field painting, Lyrical Abstraction, Fluxus, Pop Art, Minimalism, Postminimalism, and Neo-expressionism. Pop artists such as Andy Warhol and Minimalists such as Donald Judd and Agnes Martin developed in direct response to it.