A virus particle consists of a genome contained within a protein shell. This shell (the capsid) plays multiple roles throughout the infectious cycle, from genome protection to host recognition to successful genome delivery. When capsids first assemble in the cell, most often an initial product is obtained that has not achieved its fully infectious form. To do so, it must undergo a final process called maturation. Virus maturation entails conformational and stability changes. These changes are often driven by proteolytic cleavages, and their main purpose is to ensure successful delivery of the virus genome to a new host cell. Recent advances in molecular, structural, and physical virology techniques are providing a wealth of detailed information and new points of view to understand the principles of virus maturation. Evidence showing that viral capsids are built with a limited set of structural solutions has prompted a new virus classification in structural lineages deriving from a few initial ancestors. This chapter summarizes the current knowledge on maturation for the main virus structural lineages, as well as for other relevant viruses not assigned to any particular lineage yet.