Avulsions remain a critical but understudied aspect of debris-flow fans and flow hazard. A substantial body of work on fluvial systems provides a conceptual framework for understanding avulsions, but equivalent research on debris-flow systems has lagged behind. A small but growing set of field examples and analogue experiments shows that many, but not all, avulsions on debris-flow fans follow a relatively predictable 'avulsion cycle' that consists of (1) deposition of debris-flow material in the active channel, (2) backstepping of deposition toward the fan apex in one or more small- to medium-sized surges or flows, and (3) avulsion during a subsequent larger surge or flow that leaves the channel and establishes a new pathway down the fan. Debris flows tend to occupy persistent pathways on the time scale of individual flows, but over longer time scales (perhaps greater than ~5-20 flows, based on very limited data) flows tend to avulse to fill topographic lows, leading to compensational behavior. Avulsions may be encouraged by sequences of small- to medium-sized flows followed by a large flow, and discouraged by sequences of large flows in succession, although this idea remains speculative and needs to be tested. Avulsion frequency is important for understanding flow hazard but is poorly constrained, and cannot yet be predicted as a function of either flow or catchment characteristics. The advent of new, high-resolution topographic data from fan surfaces, coupled with methods to estimate the timing and abandonment of deposition on a wide range of fans, should allow us to begin to make some initial estimates of avulsion frequency and to understand the key controls on the timing and pattern of avulsions.