  We review recent work in the lattice approach to random surfaces and quantum
gravity. Our task is made somewhat easier by some very interesting results,
particularly in four dimensions, that have appeared recently and which are
reported elsewhere in these proceedings. Inevitably, given the scope of the
review and the limitations of space, the presentation will omit work of
importance and be telegraphic in discussing work that is included, for which
apologies are offered in advance. After the customary brief historical
introduction we work our way in dimensional order from one up to four
dimensions before closing with some remarks on the relation, if any, between
the various lattice models and ``real'' 4D gravity.
