Polycrystalline materials are important in many technological applications, yet there are still many challenges they present for mathematical modeling and analysis. One such challenge lies in understanding how statistical distributions develop in the process of coarsening of materials microstructure and how these distributions in turn relate to materials properties. In this talk, we will discuss and compare several recent continuum level models focusing on newly discovered features of interface dynamics that connect this problem to the theory of Markov processes in industrial applications and Boltzmann equations in statistical physics. Numerical results obtained by both models will be compared against those produced by experiments and large-scale simulations.