The boundary of a spin foam is a spin network, just as in the theory of manifolds, where the boundary of an n-manifold is an (n-1)-manifold.

In loop quantum gravity, the present spin foam theory has been inspired by the Ponzano-Regge model. The idea was introduced by Reisenberger and Rovelli in 1997, and later developed into the Barrett-Crane model. The formulation that is used nowadays is commonly called EPRL