Technical details are outside the scope of this FAQ, but you can find
an introduction and references for further reading in the comp.compression
FAQ, which is available from http://www.faqs.org/faqs/compression-faq/
(see also "[24] Where are FAQ lists archived?").

The comp.compression FAQ is also a good starting point for information on
other state-of-the-art image compression methods, such as wavelets and
fractals.  A quick comparison: wavelets are likely to be the basis of the
next generation of lossy image-compression standards, but they are perhaps
10 years behind JPEG in the standardization pipeline.  Fractals have been
terribly over-hyped by their chief commercial proponent, and seem to be
losing favor as people learn more about their true capabilities and
limitations.