Both BMI and ASCAP, as well as other organizations like SESAC monitor performances of the music to which they control the rights and collect and distribute royalties.
Radio stations originally only broadcast performers live, the performers working for free. Later performers wanted to be paid and recordings became more palatable. Many composers didn't want their music performed or played for free, but the stations wouldn't pay them. The composers who were members of the American Society of Composers, Authors, and Publishers, boycotted radio in 1944. The stations established a competing source of music, Broadcast Music Incorporated, BMI. Many stations also joined one of the NBC networks, Red or Blue, to lower production costs. (The NBC Blue network later became ABC.)
Although it is not a hard and fast rule, ASCAP has been more identified with established professional composers from Hollywood, Broadway, and Tin Pan Alley, while BMI represents less established composers. In more recent times, many of the more successful composers in these genres have joined ASCAP. Some have publishing companies in both camps.
ASCAP has an extensive awards program: Country Music, Concert Music, Primetime Emmy, World Soundtrack, MTV Music Video, Pop, Rhythm and Soul Music, Film and Television, El Premio, Dove, Christian Music, Academy of Country Music, Academy, NAACP Image, Stellar, Soul Train, Grammy, Billboard Music, Golden Globe, and American Music.