Granular materials display a host of fascinating behaviours both remarkably similar to and strikingly different from those exhibited by classical solids, liquids and gases. Due to the ubiquity of granular materials, and their far-reaching importance in multitudinous natural and industrial processes, an understanding of their dynamics is of the utmost importance to modern society. In this thesis, we analyse in detail two phenomena, one from each of the above categories: granular convection, a behaviour directly analogous to the Rayleigh-Benard cells observable in classical fluids, and granular segregation, a phenomenon without parallel in classical, molecular physics, yet which is known to greatly impact various physical and industrial systems. Through this analysis, conducted using a combination of the experimental positron emission particle tracking technique and discrete particle method simulations, we aim to improve our knowledge of these processes on a fundamental level, gaining insight into the factors which may influence them, and hence how they may be effectively controlled, augmented or eliminated.