Dense granular flows are observed in a wide range of natural phenomena, such as debris flows, snow avalanches and dense pyroclastic flows, to small-scale chute flows that are used extensively in industry. Understanding the underlying physics of such systems is of great importance to avoid waste and essential for developing hazard mit- igation strategies. In this thesis, two processes are investigated: Self-channelisation in monodisperse flows and the effect of particle size segregation on the kinematics of granular roll waves. Firstly, we consider the problem of self-channelisation that occurs when a monodisperse granular material is supplied onto an inclined rough plane with a constant injection rate and, as the front propagates downstream, the edges of the flow spontaneously solidify to form static levees, confining a central flowing channel. A viscous depth-averaged avalanche model is used to show that two physical mecha- nisms are crucial to uniquely select the equilibrium state and quantitatively predict the self-channelisation process, namely frictional hysteresis and depth-averaged lateral viscous dissipation. Importantly, it is shown that the steady configuration is governed by a well-defined force balance, which implies that the width of leveed channels is not necessarily set by the granular front. Time-dependent simulations are performed to investigate the transient evolution towards the equilibrium state, as well as how the system transitions to an unsteady avalanching regime as the mass flux is reduced. We proceed by investigating a monodisperse granular flow over a rough conical surface. Small-scale experiments show that down the cone the granular material spreads, thins and slows down until the interface splits, generating a beautiful fingering pattern, in which each individual finger has the morphology of a self-channelised flow. Numerical solutions of the depth-averaged model are used to predict the position at which the interface breaks, as well as the number of fully developed fingers, demonstrating that granular fingering is possible in monodisperse flows due to the hysteretic nature of the particulate media. The second problem addressed in this thesis regards the formation of roll waves in bidisperse granular avalanches. This is investigated through experi- ments with two different-sized spherical beads confined between rigid glass sidewalls. Using a depth-averaged segregation model, we construct travelling-wave solutions for the bulk flow and show that different regimes are possible for the particle concen- tration profile. Time-dependent simulations qualitatively recover the experiments, showing that a concertina-like effect results in a higher concentration of larger and more friction particles at the wave crests. Both phenomena here studied can lead to a significant increase in the destructive potential of large-scale flows and, therefore, our results may be particularly relevant in the geophysical context.