  We provide a Hochster type formula for the local cohomology modules of
binomial edge ideals. As a consequence we obtain a simple criterion for the
Cohen-Macaulayness of these ideals and we describe their Castelnuovo-Mumford
regularity and their Hilbert series. We also prove a conjecture of Conca, De
Negri and Gorla relating the graded components of the local cohomology modules
of binomial edge ideals and their generic initial ideals.
