Structural studies of viruses that are investigated as part of a program to understand molecular machines are described. Crystallography, solution X-ray scattering, electron microscopy and molecular virology were employed to investigate structure, assembly and maturation of RNA and dsDNA viruses. 240 copies of the RNA viral subunits (each with 650 amino acids) spontaneously assemble at pH 7 in a baculovirus expression system to form T = 4 icosahedral particles, 450 A in diameter. At pH 5 the particles condense to 410 A and the subunits auto-catalytically cleave at residue 570. 420 copies of the dsDNA viral subunits (281 amino acids each) assemble in an E. coli expression system to form T = 7 icosahedral particles, 450 A in diameter. At pH 4 the particles expand to 650 A diameter with the auto-catalytic formation of cross links between a lysine side chain and an asparagine side chain creating a concatenated set of 60 hexamer and 12 pentamer rings rendering the particle impervious to denaturation without protease treatment. Moderate- to high-resolution structures of the procapsids and capsids of these virus particles have been determined as well as cryoEM reconstructions of intermediate structures in order to define the driving force and the trajectories of these large-scale transitions.