  Deza digraphs were introduced in 2003 by Zhang and Wang as directed graph
version of Deza graphs, that also generalize the notion of directed strongly
regular graphs. In this paper we give several new constructions of Deza
digraphs. Further, we introduce twin and Siamese twin (directed) Deza graphs
and construct several examples. Moreover, we classify directed Deza graphs with
parameters $(n,k,b,a,t)$ having the property that $b=t$. Finally, we introduce
a variation of directed Deza graphs and provide a construction from finite
fields.
