Quantum gravity as quantum field theory of simplicial geometry?

I present a brief overview of the group field theory approach to quantum gravity, leading to a complete definition of spin foam models including a sum over triangulations of spacetimes of all topologies. These models are non-perturbative and fully background independent. Here gravity, and therefore spacetime geometry, is described in purely algebraic (representation-theoretic) and combinatorial terms. Most important, I discuss what are, in my opinion, the pleasent features of this approach and what are the next steps needed in order to make these models not only promising but solid candidates to the final theory of quantum gravity.