Analyzing the microstructure of cellular materials allows for a better understanding of their macroscopic properties. These properties can be studied via numerical simulations for which accurate microstructure models are necessary. Tessellations subdivide space into cells. This motivates the use of (random) tessellations for modelling cellular materials. 

An important class of tessellation models are Voronoi tessellations and their generalizations. They are generated based on a locally finite set of generators. Every point in space is then assigned to its nearest generator. The distances are measured according to some distance function. Depending on the chosen
distance function, several tessellation models can be defined. For example, the Voronoi tessellation is obtained when using the Euclidean distance. Its cells are convex polytopes. Generalizations of the Voronoi tessellation include tessellations with possibly non-convex cells with curved boundaries. 

The goal of modelling a cellular microstructure is to define a suitable model whose realizations resemble the observed structure. Fitting the real microstructure well, in particular meeting essential geometric features like cell size and shape distributions, is crucial for the quality of predictions of macroscopic properties based on microstructural simulations. This contribution gives an overview over several modelling strategies. They can be categorized into three groups. First, parametric stochastic modelling approaches aim at fitting a parametric model to the structure, for example a Laguerre tessellation that is generated by a packing of spheres with lognormal radius distribution. Second, the goal of stochastic reconstruction is to find model realizations which are statistically equivalent to the observed structure, for example regarding the cell size and aspect ratio distributions. Third, approximation is the task of finding a set of generators such that the resulting tessellation approximates the observed structure as good as possible with respect to a suitable discrepancy measure.