  In the causal set approach to quantum gravity the spacetime continuum arises
as an approximation to a fundamentally discrete substructure, the causal set,
which is a locally finite partially ordered set. The causal set paradigm was
elucidated in a classic paper by Bombelli, Lee, Meyer and Sorkin in 1987. While
early kinematical results already showed promise, the program received a
substantial impetus about a decade ago with the work of Rideout and Sorkin on a
classical stochastic growth dynamics for causal sets. Considerable progress has
been made ever since in our understanding of causal set theory while leaving
undisturbed the basic paradigm. Recent highlights include a causal set
expression for the Einstein-Hilbert action and the construction of a scalar
field Feynman propagator on a fixed causal set. The aim of the present article
is to give a broad overview of the results in causal set theory while pointing
out directions for future investigations.
