The purpose of this is a short survey of the theory of Ramanujan graphs. Ramanujan graphs have considerable importance in view of the fact that they have optimal spectral expansion and hence can be adopted as interconnection networks and error-correcting codes. M. Ram Murti describes in his paper, Ramanujan graphs as it fuses diverse branches of pure mathematics namely number theory, representation theory, and algebraic geometry. We briefly discuss how these are related and how certain Cayley graphs are considered examples of Ramanujan graphs and how their spectrum is analyzed. We also consider some explicit constructions of infinite families of Ramanujan graphs. Also, discuss the circumstance when certain families of become Ramanujan.