  Ramanujan graphs are graphs whose spectrum is bounded optimally. Such graphs
have found numerous applications in combinatorics and computer science. In
recent years, a high dimensional theory has emerged. In this paper these
developments are surveyed. After explaining their connection to the Ramanujan
conjecture we will present some old and new results with an emphasis on random
walks on these discrete objects and on the Euclidean spheres. The latter lead
to "golden gates" which are of importance in quantum computation.
