Preparing a texture suitable for a given purpose is a central problem in materials science, which presents many challenges for mathematical modeling, simulation, and analysis. In this talk, I will focus on the mesoscopic behavior of the grain boundary system and on understanding the role of topological reconfigurations during evolution. Several types of evolution equations based on pure probabilistic and stochastic descriptions will be formulated and compared against the results provided by simulation. Their advantages and limitations, numerical characteristics and possible extensions to higher dimensions will be discussed.