In the broadest sense, contemporary music is any music being written in the present day. In the context of classical music the term applies to music written in the last half century or so, particularly works post-1960. The argument over whether the term applies to music in any style, or whether it applies only to composers writing avant-garde music, or "modernist" music is a subject of hot debate. There is some use of "Contemporary" as a synonym for "Modern", particularly in academic settings, whereas others are more restrictive and apply the term only to presently living composers and their works. Since it is a word that describes a time frame, rather than a particular style or unifying idea, there are no universally agreed on criteria for making these distinctions.
In the early part of the 20th century contemporary music included modernism, the twelve tone technique, atonality, unresolved and greater amounts of dissonance, rhythmic complexity and neoclassicism. In the '50s contemporary music generally meant serialism, in the '60s serialism, indeterminacy, electronic music including computer music, mixed media, performance art, and fluxus, and since then minimal music, post-minimalism, and all of the above.
Since the 1970s there has been increasing stylistic variety, with far too many schools to name or label. However, in general, there are three broad trends. The first is the continuation of modern avant-garde traditions, including musical experimentalism. The second are schools which sought to revitalize a tonal style based on previous common practice. The third focuses on non-functional triadic harmony, exemplified by composers working in the minimalist and related traditions.
Contemporary music composition has been altered with growing force by computers in composition, which allow for composers to listen to renderings of their scores before performance, compose by layering performed parts over each other and to disseminate scores over the internet. It is far too soon to tell what the final result of this wave of computerization will have as an effect on music.
All history is provisional, and contemporary history even more so, because of the well known problems of dissemination and social power. Who is "in" and who is "out" is often more important to who is known than the music itself. In an era with perhaps has many as 40,000 composers of concert music in the United States alone, first performances are difficult, and second performances even more so. The lesson of obscure composers in the past becoming important later applies doubly so to contemporary music, where it is likely that there are "firsts" before the officially listed first, and works which will be later admired as exemplars of style, which are as yet, unheralded in their own time.