Claude Debussy, one of the most successful composers at the beginning of the 20th century, stitched together an income from public performances as both pianist and conductor, from publication of his music, and from writing music criticism. As the 20th century wore on, however, and as composers more and more drifted into a musical language that was more and more difficult for audiences to absorb, they came to depend on teaching, taking posts as professors of composition, and on commissions from institutions ultimately funded by governments. In Canada, for example, most composers are either employed by universities or conservatories to teach theory and composition, or survive on Canada Council grants and commissions. There is a network of Canadian Music Centres nationwide that contain libraries of scores by Canadian composers that may be loaned to performers.
From the 1970s, a few composers began to appeal to wider audiences, Philip Glass and Steve Reich in particular, and stayed out of academe by creating their own performing ensembles, winning commissions and making enough recordings to flourish as composers.
Now, in the 21st century, these models will continue, but we are likely to see new ones. The young American composer Nico Muhly, for example, has worked in collaboration with both Björk and Philip Glass. He manages to combine collaborations with popular musicians with commissions from classical ensembles.
One final note: for those of you who have wondered about the revisions of some of Stravinsky's early works decades later, perhaps the main reason for this was that, under the Soviet law of the time, the copyrights on these works were going to expire and this was a way of extending the copyright. Petrushka, written in 1911, was revised in 1947, largely for this reason.