Particles immersed in a fluid excite long-ranged flows as they move, and similarly move in response to fluid motion. By generating and reacting to a fluid's local velocity, colloidal particles experience hydrodynamic interactions with each other and with the walls of their container. Despite its long-recognized ubiquity, such hydrodynamic coupling is incompletely understood. This section addresses the hydrodynamically coupled dynamics of well-separated particles moving slowly through a viscous fluid, a comparatively simple limiting case of considerable practical importance. In particular, it applies the method of singularities , also known as stokeslet analysis, to the hydrodynamics of small colloidal systems and compares the results to recent measurements. The favorable outcome suggests that stokeslet analysis offers a tractable, general, and scalable formulation for many-body colloidal hydrodynamics.