In this exposition we give a simple and complete treatment of A. Knutson and T.
Tao's recent proof (http://front.math.ucdavis.edu/math.RT/9807160) of the saturation
conjecture, which asserts that the Littlewood-Richardson semigroup is saturated. The main
tool is Knutson and Tao's hive model for Berenstein-Zelevinsky polytopes. In an appendix of
W. Fulton it is shown that the hive model is equivalent to the original