  While there has been some advance in the use of Regge calculus as a tool in
numerical relativity, the main progress in Regge calculus recently has been in
quantum gravity. After a brief discussion of this progress, attention is
focussed on two particular, related aspects. Firstly, the possible definitions
of diffeomorphisms or gauge transformations in Regge calculus are examined and
examples are given. Secondly, an investigation of the signature of the
simplicial supermetric is described. This is the Lund-Regge metric on
simplicial configuration space and defines the distance between simplicial
three-geometries. Information on its signature can be used to extend the rather
limited results on the signature of the supermetric in the continuum case. This
information is obtained by a combination of analytic and numerical techniques.
For the three-sphere and the three-torus, the numerical results agree with the
analytic ones and show the existence of degeneracy and signature change. Some
``vertical'' directions in simplicial configuration space, corresponding to
simplicial metrics related by gauge transformations, are found for the
three-torus.

General Relativity and Quantum Cosmology