Debris flows can be highly destructive and pose a significant threat to both life and property in those areas in which they naturally occur. Such flows can be especially hazardous when large amplitude surges form, which cause more damage than continuous flows of the same mass flux. It is therefore important to understand how these surges form and subsequently behave.The most likely explanation for their formation is the spontaneous development of roll waves - small shock-like disturbances typically observed in thin liquid films - which merge and coarsen as they travel downslope, in turn growing in amplitude and wavespeed.There have also been observations of naturally occurring debris flows which develop surges with regions of completely stationary material between them. The terminology of 'erosion-deposition' waves is introduced to describe these waves, according to the process by which they propagate steadily through a flow by eroding at the static layer ahead of the wave front and depositing a stationary layer behind it. This behaviour is particularly novel and the pulses can be even more destructive than their roll wave counterparts.A combination of experimental observations, travelling-wave solutions and numerical simulations are used here to study the behaviour of both roll waves and erosion-deposition waves in granular flows.