Joint work with H. Reid, L. Zhang, C. Coelho, Z. Zhu, T. Klemas, and S. Johnson. Despite decades of zealous effort, there are remarkably few applications where fast integral equation solvers dominate. To help explain why, we will describe effective strategies, assess performance, and present remaining challenges associated with applying fast solvers to problems in interconnect model extraction, biomolecular electrostatics, bodies in microflows, nanophotonics, and Casimir force calculation.