Free-surface flows of non-Newtonian fluids are mainly shaped by the interplay between gravity (the driving force) and the fluid's viscous nature (rheology), giving rise to behaviors that range from smooth creeping motion to sudden surges and wave-like instabilities. Understanding the dynamics of such flows is crucial for describing natural mass movements such as mudflows and debris flows, and for improving predictive tools in hydraulic and environmental modeling. Theoretical models extend classical shallow-water equations by incorporating Herschel–Bulkley rheology, facilitating the study of transitions between solid-like and fluid-like states and the influence of yield stress and bed geometry on flow profiles and dynamics. The emergence of roll-wave instabilities, periodic hydrodynamic structures arising from imbalances between inertia and resistance on a flat bed, can be analyzed using linear stability analysis of these models. Critical conditions for their development and the role of rheology in governing their growth and propagation are identified. Additionally, from an experimental perspective, pressure reconstruction techniques based on Particle Image Velocimetry (PIV) can enable detailed examination of pressure fields in viscoplastic flows, including unyielded regions such as dead and plug zones.