  The BPS state spectrum in four-dimensional gauge theories or string vacua
with N=2 supersymmetries is well known to depend on the values of the
parameters or moduli at spatial infinity. The BPS index is locally constant,
but discontinuous across real codimension-one walls where some of the BPS
states decay. By postulating that BPS states are bound states of more
elementary constituents carrying their own degrees of freedom and interacting
via supersymmetric quantum mechanics, we provide a physically transparent
derivation of the universal wall-crossing formula which governs the jump of the
index. The same physical picture suggests that at any point in moduli space,
the total index can be written as a sum of contributions from all possible
bound states of elementary, absolutely stable constituents with the same total
charge. For D-brane bound states described by quivers, this `Coulomb branch
formula' predicts that the cohomology of quiver moduli spaces is uniquely
determined by certain `pure-Higgs' invariants, which are the microscopic
analogues of single-centered black holes. These lectures are based on joint
work with J. Manschot and A. Sen.
