  In this paper, we give a classification of all compact Hermitian manifolds
with flat Bismut connection. We show that the torsion tensor of such a manifold
must be parallel, thus the universal cover of such a manifold is a Lie group
equipped with a bi-invariant metric and a compatible left invariant complex
structure. In particular, isosceles Hopf surfaces are the only Bismut flat
compact non-K\"ahler surfaces, while central Calabi-Eckmann threefolds are the
only simply-connected compact Bismut flat threefolds.
