  In this expository paper we describe a group theoretic characterization of
arc-transitive graphs and their quotients. When passing from a symmetric graph
to its quotient, much information is lost, but some of this information may be
recovered from a certain combinatorial design on the blocks, as well as a
bipartite graph between the blocks. We address the "extention problem" which
asks, when is this additional information sufficient to recover the original
graph?
