Self-assembly (SA) is the process in which a system's components—be it molecules, polymers, colloids, or macroscopic particles—organize into ordered and/or functional structures without human intervention. The main challenge in SA research is the ability to “program” the properties of the individual pieces such that they organize into a desired structure. Although a general strategy for doing so is still elusive, heuristic rules can be formulated that guide design of SA under various conditions and thermodynamic constraints. This Review examines SA in both the equilibrium and non-equilibrium/dynamic systems and discusses different SA modalities: energy driven, entropy-driven, templated, and field-directed. Non-equilibrium SA is discussed as a route to reconfigurable (“adaptive”) materials, and its connection to biological systems is emphasized.