Abstract: Interacting particle systems (IPSs) are stochastic models for the temporal evolution of spatially extended systems. While they were developed initially to analyze numerically equilibrium behavior in statistical physics, it has become clear in the meantime that IPSs are valuable non-equilibrium models in their own right. In particular, they prove more and more to be appropriate in another field of application: biological systems which are by nature open, non-equilibrium systems where noise is ubiquitous. Considering the field of developmental biology, an important application area for IPSs is the analysis of the emergent collective behavior that results from local interactions of biological cells. When cells react to their surrounding, neighboring cells as well as extracellular matrix and other environmental influences, with type-specific differences, what are the emergent properties for the whole tissue? For exemplary problems, IPS models are proposed and studied which describe the major details of the respective intercellular interaction. Several results concerning the long-time behavior and the emergence of structure at the tissue scale are presented and interpreted in biological terms. Mathematical challenges that require further theoretical developments are identified.