The past few years have seen an explosion in the number of viral structures determined by icosahedral reconstruction from cryoelectron micrographs. The success of this work has depended upon a combination of the high-fidelity but low-contrast information contained in these images with efficient algorithms for determining particle orientation and three-dimensional structure. This review describes the principles behind the most commonly used method of reconstruction of the icosahedral particles and the method's implementation in an icosahedral reconstruction program suite. (C) 1996 Academic Press, Inc.