  Spin foams provide path integrals for quantum gravity, which employ
discretizations as regulator. To obtain regulator independent predictions, we
must remove these fiducial structures in a suitable refinement limit. In this
chapter we present the current state of research: We begin with a discussion on
the role of diffeomorphism symmetries in discrete systems, the notion of scale
in background independent theories and how we can consistently improve theories
via renormalization to reduce regulator dependence. We present the consistent
boundary formulation, which provides a renormalization framework for background
independent theories, and discuss tensor network methods and restricted spin
foams, which provide concrete renormalization algorithms aiming at the
construction of consistent boundary amplitudes for spin foams. We furthermore
discuss effective spin foams, which have allowed for the construction of a
perturbative refinement limit and an associated effective continuum action.
