From discrete causal sets to a spacetime continuum

We understand reasonably well how to construct a discrete causal set that approximates a given spacetime manifold. The vast majority of causal sets, though, are not at all continuum-like, and if we take the discrete description to be fundamental, we must somehow suppress these "bad" sets. I will discuss some recent progress in showing that a very large class of non-manifoldlike sets is extremely strongly suppressed in the ordinary gravitational path integral, perhaps allowing us to recover the observed continuum structure of spacetime from the quantum theory of discrete structures.