An $(n,d,\lambda)$-graph is a d-regular graph on $n$ vertices so that the absolute value of each eigenvalue of its adjacency matrix, besides the largest one, is at most $\lambda$. I will survey some of the remarkable pseudo-random properties of such graphs in which $\lambda$ is much smaller than $d$, describe various constructions, and present several applications of these graphs in the solution of problems in Extremal Combinatorics, Geometry and and Complexity.