The past few decades have seen tremendous advances in single-particle electron -cryo-microscopy (cryo-EM). The field has matured to the point that near-atomic resolution density maps can be generated for icosahedral viruses without the need for crystallization. In parallel, substantial progress has been made in determining the structures of nonicosahedrally arranged proteins in viruses by employing either single-particle cryo-EM or cryo-electron tomography (cryo-ET). Implicit in this course have been the availability of a new generation of electron cryo-microscopes and the development of the computational tools that are essential for generating these maps and models. This methodology has enabled structural biologists to analyze structures in increasing detail for virus particles that are in different morphogenetic states. Furthermore, electron imaging of frozen, hydrated cells, in the process of being infected by viruses, has also opened up a new avenue for studying virus structures "in situ". Here we present the common techniques used to acquire and process cryo-EM and cryo-ET data and discuss their implications for structural virology both now and in the future.