We present an introduction to group field theories and tensor models, as a framework for the dynamics of quantum spacetime. They are a generalization of matrix models for 2d quantum gravity, incorporating insights from other approaches like spin foam models and simplicial quantum gravity, as well as tools from non-commutative geometry. We review briefly recent developments, and discuss in more detail some of them.

Max-Planck-Institut für Gravitationsphysik, Golm, DE