Short answers, pulled from the story.
20th-century classical music was unique in having no single dominant style. Musical style diverged more radically than in any previous century, producing an unprecedented "linguistic plurality" of techniques including atonality, serialism, musique concrète, minimalism, and electronic music, all within a single hundred-year period.
Arnold Schoenberg developed the twelve-tone technique after several years of research, first describing it privately to associates in 1923. His first large-scale work composed entirely using the method was the Wind Quintet, Op. 26, written in 1923-24. His students Alban Berg and Anton Webern, and later Pierre Boulez, developed the technique further.
Musique concrète is a form of composition that uses recorded acoustical sounds from the everyday world as its raw material. Pierre Schaeffer pioneered it in the 1940s and 50s. It was later grouped under the broader category of electroacoustic music, which also covers music made with electronic generators, magnetic tape, computers, and synthesizers.
Minimalism strips music down to its most fundamental features, often using repetition and iteration. Key composers include La Monte Young, Arvo Pärt, Philip Glass, Terry Riley, Steve Reich, and John Adams. An early example is Terry Riley's In C from 1964, in which musicians choose short phrases from a set list and play each an arbitrary number of times.
Jazz became a major influence on composers including George Gershwin, Leonard Bernstein, Darius Milhaud, Aaron Copland, Maurice Ravel, Dmitri Shostakovich, and Igor Stravinsky, who each produced concert works drawing on jazz idioms. Milhaud's La création du monde and Bernstein's West Side Story are named examples. Jazz musicians including Duke Ellington, Gil Evans, Art Tatum, and Cecil Taylor were in turn influenced by the impressionist musical language.
Futurism, founded by Filippo Tommaso Marinetti in 1909, called for the incorporation of noise into music, as set out in Luigi Russolo's 1913 manifesto L'arte dei rumori. Though few original futurist works are performed today, the movement's lasting influence includes the prepared piano, integral serialism, extended vocal techniques, graphic notation, improvisation, and minimalism.