  In this paper we extend the notion of digraphical regular representations in
the context of Haar digraphs. Given a group $G$, a {\em Haar digraph} $\Gamma$
over $G$ is a bipartite digraph having a bipartition $\{X,Y\}$ such that $G$ is
a group of automorphisms of $\Gamma$ acting regularly on $X$ and on $Y$. We say
that $G$ admits a {\em Haar digraphical representation} (HDR for short), if
there exists a Haar digraph over $G$ such that its automorphism group is
isomorphic to $G$. In this paper, we classify finite groups admitting a HDR.
