Viruses are elegant macromolecular assemblies and constitute a paradigm of the economy of genomic resources; they must use simple general principles and a very limited number of viral components to complete their life cycles successfully. Viruses need only one or a few different capsid structural subunits to build an infectious particle, which is made possible because of two reasons: extensive use of symmetry and built-in conformational flexibility. Although viruses from the numerous virus families come in many shapes and sizes, two major types of symmetric assemblies are found: icosahedral and helical particles. The enormous diversity of virus structures might be derived from one or a limited number of basic schemes that has become more complex by consecutive incorporation of structural elements. The intrinsic structural polymorphism of the viral proteins and other observations indicate that capsids are dynamic structures. Study of virus structures is required to understand structure-function relationships in viruses, including those related to morphogenesis and antigenicity. These structural foundations can be extended to other macromolecular complexes that control many fundamental processes in biology.