ATRAC (Adaptive TRansform Acoustic Coding) is a proprietary audio compression technology developed by Sony for usage in their MiniDisc line of digital audio players. It actually relates to three different audio compression technologies related among themselves, but with incompatibilities. It uses quadrature mirror filters and modified discrete cosine transform to represent encoded audio.
ATRAC (also called ATRAC1) was developed in 1991, and used in the first MiniDisc players in the early nineties. It used bitrates of 292kbps for stereo audio and 146 for mono. Several subversions were released, from 1 to 4.5, and all of them are backwards and forwards compatible. It's reported that it only started sounding good after version 3.
ATRAC3 was released by Sony in 2000. It offers much better performance than ATRAC1, with reasonable quality at 132kbps. It's not backwards compatible with ATRAC1.
In 2003, Sony released ATRAC3plus, the third backwards-incompatible revision of their codec. They promise to deliver transparency at 48kbps with this new codec (of course, that's an absurd claim).