CRISPR (cluster of regularly interspaced palindromic repeats) is a prokaryotic adaptive defence system, providing immunity against mobile genetic elements such as viruses. Genomically encoded crRNA (CRISPR RNA) is used by Cas (CRISPR-associated) proteins to target and subsequently degrade nucleic acids of invading entities in a sequence-dependent manner. The process is known as ‘interference’. In the present review we cover recent progress on the structural biology of the CRISPR/Cas system, focusing on the Cas proteins and complexes that catalyse crRNA biogenesis and interference. Structural studies have helped in the elucidation of key mechanisms, including the recognition and cleavage of crRNA by the Cas6 and Cas5 proteins, where remarkable diversity at the level of both substrate recognition and catalysis has become apparent. The RNA-binding RAMP (repeat-associated mysterious protein) domain is present in the Cas5, Cas6, Cas7 and Cmr3 protein families and RAMP-like domains are found in Cas2 and Cas10. Structural analysis has also revealed an evolutionary link between the small subunits of the type I and type III-B interference complexes. Future studies of the interference complexes and their constituent components will transform our understanding of the system.