  The causal set theory (CST) approach to quantum gravity postulates that at
the most fundamental level, spacetime is discrete, with the spacetime continuum
replaced by locally finite posets or "causal sets". The partial order on a
causal set represents a proto-causality relation while local finiteness encodes
an intrinsic discreteness. In the continuum approximation the former
corresponds to the spacetime causality relation and the latter to a fundamental
spacetime atomicity, so that finite volume regions in the continuum contain
only a finite number of causal set elements. CST is deeply rooted in the
Lorentzian character of spacetime, where a primary role is played by the causal
structure poset. Importantly, the assumption of a fundamental discreteness in
CST does not violate local Lorentz invariance in the continuum approximation.
On the other hand, the combination of discreteness and Lorentz invariance gives
rise to a characteristic non-locality which distinguishes CST from most other
approaches to quantum gravity.
  In this review we give a broad, semi-pedagogical introduction to CST,
highlighting key results as well as some of the key open questions. This review
is intended both for the beginner student in quantum gravity as well as more
seasoned researchers in the field.
