The goal of this expository paper is to introduce De Bruijn graphs and discuss their applications to fault tolerant networks. We will begin by examining N.G. de Bruijn's original paper and the proof of his claim that there are exactly  De Bruijn cycles in the binary De Bruijn graph B(2, n). In order to study fault tolerance we explore the properties of Hamiltonian and Eulerian cycles that occur on De Bruijn graphs and the type of redundancy that occurs as a result. Lastly, in this paper we seek to provide some guidance into further research on De Bruijn graphs and their potential applications to other areas.