The STIT tessellation (stochastically STable under the operation of ITeration of tessellations) process is a Markov process where the states are tessellations of the plane or a higher-dimensional Euclidean space. The transition to a new state is caused by a random division of individual cells, where each cell has a random life time, and at the end of its life it is randomly divided. This particular cell division model was introduced by W. Nagel and V. Weiss (2005), and meanwhile a series of papers with quite a few theoretical results is published. In the talk, a survey of important features of the STIT model is given. The focus is on spatial mixing properties which also yield bounds for the variances of certain entities of these tessellations (joint work with S. Martínez).