Why do musical styles change? The evolution of musical styles is certainly somewhat a result of the influence individual composers have on one another. Unfortunately, this influence isn't always positive. Sometimes, the work of a composer is a reaction against the style practiced by his predecessors, even when theyadmire the music they produced. An example of this could be drawn from the relationship of the Classical era to the Baroque era which it followed, personified by the relationship of the music of J.S. Bach and his sons.
The late Romantic era had its extremes: it seems that it used the greatest possible extent of harmonies and melodies and that the progression of the art had reached the limits of possibility. It's certainly possible to see the music of the 20th century as a continuation of the Romantic style, but it can also be interpreted as a reaction against Romanticism.
The music of the 20th century is a series of 'isms' and 'neo-isms'. The rough energy of Stravinsky's The Rite of Spring was labelled neoprimitivism; the extreme emotional tones of early Schönberg were given the label expressionism; the return to cleanly structured forms and textrues was called neoclassicism. All of these labels came (and are coming) as an attempt at orientation in the heterorogenous world of music in the 20th century.
During the first half of the 20th century, nationalism continued to have a large influence, the study of folk songs enriched the nusic of many composers, such as that of Ralph Vaughan Williams (England), Bela Bartok (Hungary), Heitor Villa Lobos (Brazil) and Aaron Copland (USA). Jazz and popular music also had a strong influence on many "serious" composers, whether in America or Europe.
The advance of technology has also had an enormous impact on the evolution of music in this century, with some composers using, for instance, the cassette player as a compositional tool (ie. Violin Phase by Steve Reich), or electronically generated sounds alongside classical instruments, the use of computers to compose music, and so on.