Localized spot patterns, where one or more solution components concentrates at discrete points in the domain, are a common class of localized pattern for reaction-diffusion systems, and they arise in a wide range of modeling scenarios. A theoretical study of such patterns in a 3-D setting is, largely, a new frontier. In an arbitrary bounded 3-D domain, the existence, linear stability, and slow dynamics of localized multi-spot patterns is analyzed for the well-known singularly perturbed Gierer-Meinhardt (GM) and Schnakenberg systems in the limit of a small activator diffusivity. Depending on the range of parameters, spot patterns can undergo competition instabilities, leading to spot-annihilation events, or shape-deforming instabilities triggering spot self-replication. In the absence of these instabilities, spots evolve slowly according to an ODE gradient flow, given by a discrete energy defined in terms of the reduced-wave Green's function. Open problems for localization on higher co-dimension structures are discussed.