  After a brief chronological sketch of developments in non-perturbative
canonical quantum gravity, some of the recent mathematical results are
reviewed. These include: i) an explicit construction of the quantum counterpart
of Wheeler's superspace; ii) a rigorous procedure leading to the general
solution of the diffeomorphism constraint in quantum geometrodynamics as well
as connection dynamics; and, iii) a scheme to incorporate the reality
conditions in quantum connection dynamics. Furthermore, there is a new language
to formulate the central questions and techniques to answer them. These
developments put the program on a sounder footing and, in particular, address
certain concerns and reservations about consistency of the overall scheme.
