  In this paper we survey existing results on Deza graphs and give some new
results. We present an introduction to Deza graphs for the reader who is
unfamiliar with the subject, and then give an overview of some developments in
the area of Deza graphs since the initial paper by five authors [M. Erickson,
S. Fernando, W. H. Haemers, D. Hardy, J. Hemmeter, Deza graphs: \emph{A
generalization of strongly regular graphs}, J. Comb. Designs. 7 (1999),
395--405.] was written. We then investigate 3-class cyclotomic schemes and give
necessary and sufficient conditions to get a Deza graph as a graph given by one
relation or the union of two relations. Finally, we prove that a strictly Deza
circulant on $2p$ vertices, where $p$ is prime, is isomorphic to the
lexicographical product of the Paley graph on $p$ vertices with an edge.
