LAUSR

We review the topological invariants that count supersymmetric states for gauge theories, with an emphasis on string theory applications. In particular, the enumerative index and the twisted partition functions are carefully distinguished by how continuum sectors are handled. The recent localization routine has led to a systematic computation of the latter, and we offer a mechanism for extracting the truly enumerative indices when the continuum sector originates in the Coulomb branch. This leads to a satisfactory conclusion of a twenty-year saga of D0-brane bound state problems. We close with broad comments on how the wall-crossing manifests in the index theorems, and define the Quiver/GLSM invariants, which are entirely immune under the wall-crossing.