Subduction zone earthquakes result in some of the most devastating natural hazards on Earth. Knowledge of where great (moment magnitude M ≥ 8) subduction zone earthquakes can occur and how they rupture is critical to constraining future seismic and tsunami hazards. Since the occurrence of well-instrumented great earthquakes, such as the 2004 M9.1 Sumatra–Andaman and 2011 M9.1 Tohoku earthquakes, the hypotheses that plate age and convergence rate influence the ability of subduction zones to host large earthquakes have been dispelled. In this Review, we highlight how certain subduction zone properties might influence the location and characteristics of great earthquake rupture and impact seismic and tsunami hazard. The rupture characteristics of great earthquakes that most heavily impact earthquake hazards include the rupture extent (seaward and landward), location of strong motion-generating areas and earthquake recurrence. By contrast, large slip or displacement at the seafloor is one of the major controls of tsunami hazard. Future improvements in addressing hazards posed by subduction zones depend heavily on sustained geophysical monitoring in subduction zone systems (both onshore and offshore), expanded development of palaeoseismic data sets and improved integration of observations and models across disciplines and timescales.