Recent Results in Causal Set Theory

In this talk I will review the basic features of causal set theory (CST) which is a discrete approach to quantum gravity. In CST one "quantizes" the causal structure poset, thus rendering it locally finite. This latter property means that continuum spacetime must be regarded as an approximation. In order to make the correspondence commensurate with results from Lorentz geometry, of a kinematic ensemble of random (Poisson distributed) causal sets. An important question is how continuum geometry and topology is encoded in the causal order. I will review results in this process of " geometric reconstruction" and related aspects, including some intriguing results on discrete entanglement entropy. I will then discuss the quantum dynamics of causal sets and summarize some recent results.