An introduction to planar random tessellation models

The goal of this paper is to give an overview of random tessellation models. We discuss the classic isotropic Poisson line tessellation in some detail and then move on to more complicated models, including Arak-Clifford-Surgailis polygonal Markov fields and their Gibbs field counterparts, crystal growth models such as the Poisson-Voronoi, Johnson-Mehl and Laguerre random tessellations, and the STIT nesting scheme. An extensive list of references is included as a guide to the literature.