Summary: In this semitutorial paper we discuss a general message passing algorithm, which we call the generalized distributive law (GDL). The GDL is a synthesis of the work of many authors in the information theory, digital communications, signal processing, statistics, and artificial intelligence communities. It includes as special cases the Baum-Welch algorithm, the fast Fourier transform (FFT) on any finite Abelian group, the Gallager-Tanner-Wiberg decoding algorithm, Viterbi's algorithm, the BCJR algorithm, Pearl's ``belief propagation'' algorithm, the Shafer-Shenoy probability propagation algorithm, and the turbo decoding algorithm. Although this algorithm is guaranteed to give exact answers only in certain cases (the ``junction tree'' condition), unfortunately not including the cases of GTW with cycles or turbo decoding, there is much experimental evidence, and a few theorems, suggesting that it often works approximately even when it is not supposed to.