Sampling-based methods arise in many statistical, computational, and engineering settings. In engineering settings, sampling can provide an easy means of constructing distributed algrorithms that scale well and avoid the need for centralized information-gathering. In computational environments, the use of sampling often leads to algorithms that have complexities that are relatively insensitive to dimensional effects, and that largely overcome the “curse of dimensionality”. In this talk, we will give an overview of these ideas and discuss some additional problem contexts within which sampling-based approaches are proving fruitful.