INO80-C and SWR-C are conserved members of a subfamily of ATP-dependent chromatin remodelling enzymes that function in transcription and genome-maintenance pathways. A crucial role for these enzymes is to control chromosomal distribution of the H2A.Z histone variant. Here we use electron microscopy (EM) and two-dimensional class averaging to demonstrate that these remodelling enzymes have similar overall architectures. Each enzyme is characterized by a dynamic 'tail' domain and a compact 'head' that contains Rvb1/Rvb2 subunits organized as hexameric rings. EM class averages and mass spectrometry support the existence of single heterohexameric rings in both SWR-C and INO80-C. EM studies define the position of the Arp8/Arp4/Act1 module within INO80-C, and we find that this module enhances nucleosome-binding affinity but is largely dispensable for remodelling activities. In contrast, the Ies6/Arp5 module is essential for INO80-C remodelling, and furthermore this module controls conformational changes that may couple nucleosome binding to remodelling.