Ubiquitin-binding domains (UBDs) are modular elements that bind non-covalently to the protein modifier ubiquitin. Recent atomic-level resolution structures of ubiquitin-UBD complexes have revealed some of the mechanisms that underlie the versatile functions of ubiquitin in vivo. The preferences of UBDs for ubiquitin chains of specific length and linkage are central to these functions. These preferences originate from multimeric interactions, whereby UBDs synergistically bind multiple ubiquitin molecules, and from contacts with regions that link ubiquitin molecules into a polymer. The sequence context of UBDs and the conformational changes that follow their binding to ubiquitin also contribute to ubiquitin signalling. These new structure-based insights provide strategies for controlling cellular processes by targeting ubiquitin-UBD interfaces.