  Let $G$ be a finite group. The bipartite divisor graph for the set of
irreducible complex character degrees is the undirected graph with vertex set
consisting of the prime numbers dividing some character degree and of the
non-identity character degrees, where a prime number $p$ is declared to be
adjacent to a character degree $m$ if and only if $p$ divides $m$. This graph
is bipartite and it encodes two of the most widely studied graphs associated to
the character degrees of a finite group: the prime graph and the divisor graph
on the set of irreducible character degrees.
  The scope of this paper is two-fold. We draw some attention to the bipartite
divisor graph for the set of irreducible complex character degrees by outlining
the main results that have been proved so far. In this process we improve some
of these results and we leave some open problems.
