Spin foam quantum gravity is a non-perturbative, background independent putative theory of quantum gravity. It is a path integral approach, i.e. a sum over histories, which is formulated as a sum over algebraic, group theoretic data encoding quantum geometry. As an introduction, I will motivate spin foams from the perspective of the canonical theory of loop quantum gravity and briefly discuss its derivation.
In the remainder of the talk, I will present successes of the approach and how we intend to address its remaining open challenges to turn it into a computational formalism. This includes the definition of a continuum limit and establishing a relation to classical physics, the numerical evaluation of spin foam amplitudes and how to define observables / model physical processes, such as cosmology.