  In this paper we will make a survey of solutions to the Wheeler-Dewitt
equation which have been found up to now in Ashtekar's formulation for
canonical quantum gravity. Roughly speaking they are classified into two
categories, namely, Wilson-loop solutions and topological solutions. While the
program of finding solutions which are composed of Wilson loops is still in its
infancy, it is expected to be developed in the near future. Topological
solutions are the only solutions at present which we can give their
interpretation in terms of spacetime geometry. While the analysis made here is
formal in the sense that we do not deal with rigorously regularized constraint
equations, these topological solutions are expected to exist even in the fully
regularized theory and they are considered to yield vacuum states of quantum
gravity. We also make an attempt to review the spin network states as
intuitively as possible. In particular, the explicit formulae for two kinds of
measures on the space of spin network states are given.
