This open access book provides graduate students and scientists with fundamental knowledge on the mechanics of granular suspensions as well as on the mathematical and numerical techniques that can be adopted to investigate geophysical flows. To this end, three formidably complex problems (sediment transport, flow-like landslide inception, and gravity currents) are considered. The reader will find a thorough combination of elements of fluid and solid mechanics, rheology, geotechnics, geomorphology, civil, and coastal engineering. The first part of the book introduces the problem of granular suspensions from the mathematical viewpoint, focusing on issues that characterise geophysical flows such as turbulence, the effects of inter-particle contacts, and strong velocity gradients. In the second part, different models that were successfully used to investigate the mechanics of granular suspensions in environmental flows are presented.