The description of a few particles with non-perturbative interactions continues to pose severe challenges in theoretical physics, although encouraging progress has been achieved. In modern day ultracold atomic, molecular, and optical physics, understanding such systems underpins our ability to control and manipulate atomic state behavior, transport, and entanglement, as well as the absorption and emission of light. In numerous contexts, there is a practical need to understand how a few particles interact, how bound clusters can form, where their resonances occur, and how to turn on or turn off loss processes or decoherence. Moreover, the study of sequences of 2,3,4,5, ... particles yields insights into many-body Hamiltonians of interest in other branches of physics. Examples of both of these avenues of theoretical few-body physics will be discussed, drawing in part from the fundamental but bizarre Efimov effect that connects a universal class of nuclear and atomic phenomena over energy scales differing by 16 orders of magnitude. Other examples will be drawn from recent explorations of a handful of interacting particles in 1, 2, or 3 dimensions, or even in mixed dimensions.