Spin foams provide models for quantum gravity and hence quantum space time. One of the key outstanding questions is to show that they reproduce smooth space time manifolds in a continuum limit.I will start with a very short introduction to spin foams and the structure of quantum space time they encode. I will explain how the investigation of the continuum limit via coarse graining and renormalization techniques led as to consider anyonic spin chains and a classification of ground states in systems with quantum group symmetries.I will then present new results on the continuum limit of spin net models, that allow us to draw first conclusions about the large scale dynamics of spin foams.
Based on: B.D., W. Kaminski, Topological lattice field theories from intertwiner dynamics, arXiv:1311.1798, B.D., S. Steinhaus, Time evolution as refining, coarse graining and entangling, to appear, B.D. M. Martin-Benito, S. Steinhaus, The refinement limit of quantum group spin net models, to appear