  We review free fermion, melting crystal and matrix model representations of
wall-crossing phenomena on local, toric Calabi-Yau manifolds. We consider both
unrefined and refined BPS counting of closed BPS states involving D2 and
D0-branes bound to a D6-brane, as well as open BPS states involving open
D2-branes ending on an additional D4-brane. Appropriate limit of these
constructions provides, among the others, matrix model representation of
refined and unrefined topological string amplitudes.
