The intestinal epithelium is permanently renewed during homoeostasis. Stable function of its stem cells is ensured by interaction with a specific tissue compartment, the so-called 'intestinal stem cell niche'. The essential regulatory principles of this niche are still under debate. In order to approach this question, we have introduced several single cell-based models of the spatiotemporal stem cell organization in murine intestinal crypts and organoids. In the present article, we provide a brief review of these models. Starting with pedigree models reproducing cell kinetics, over the last few years, we have successively improved these models by refining the biomechanical representation of the system and introducing environmentally controlled lineage specification. Our current models of the intestinal crypt are capable of linking a broad spectrum of experimental observations encompassing spatially confined cell proliferation, directed cell migration, multiple cell lineage decisions and clonal competition. Our model of intestinal organoids provides for the first time a description of a self-organizing intestinal stem cell niche. It suggests that this niche is established by secretory activity of specified cells and in addition requires a defined spatial organization, which sensitively depends on tissue biomechanics.