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.