Although there have been countertenors singing for hundreds of years, the man who made their use in music more popular was Alfred Deller. He began singing countertenor parts in baroque music in the 1950s, and gained some fame. Since then, more and more countertenors have made careers in the opera house and the recording studio.
Countertenors are most often used today in baroque operas with parts originally written for castrati. They are also heard in church music from the same period, and Benjamin Britten made the role of Oberon a countertenor in his opera, A Midsummer Night's Dream. In his distinguished career James Bowman has sung in many of Britten's works for countertenor, as well as pieces by others.
Amongst the more famous countertenors working today are Andreas Scholl and David Daniels. Yoshikazu Mera is a well known Japanese countertenor.
It should be noted that although many male rock and pop artists frequently go into falsetto and use much the same range as classical countertenors, the term is never used for them: it is essentially a name used in classical music only. (Rock and pop are generally more relaxed about categorizing types of singer anyway, and the high range of the countertenor seems likely to cause some mild confusion and embarrassment if examined too closely in the context of rock machismo.)
The term countertenor is also used much less frequently to mean a normal male tenor who uses some falsetto at the very top of his range.
A different singing technique which does not use falsetto is exploited by sopranistas.