  We give a very concise review of the group field theory formalism for
non-perturbative quantum gravity, a higher dimensional generalisation of matrix
models. We motivate it as a simplicial and local realisation of the idea of 3rd
quantization of the gravitational field, equivalently of a quantum field theory
of simplicial geometry, in which also the topology of space is fully dynamical.
We highlight the basic structure of the formalism, and discuss briefly various
models that are being studied, some recent results and the many open issues
that future research should face. Finally, we point out the connections with
other approaches to quantum gravity, such as loop quantum gravity, quantum
Regge calculus and dynamical triangulations, and causal sets.
