Dynamic self-assembly (DySA) processes occurring outside of thermodynamic equilibrium underlie many forms of adaptive and intelligent behaviors in natural systems. Relatively little, however, is known about the principles that govern DySA and the ways in which it can be extended to artificial ensembles. This article discusses recent advances in both the theory and the practice of nonequilibrium self-assembly. It is argued that a union of ideas from thermodynamics and dynamic systems' theory can provide a general description of DySA. In parallel, heuristic design rules can be used to construct DySA systems of increasing complexities based on a variety of suitable interactions/potentials on length scales from nanoscopic to macroscopic. Applications of these rules to magnetohydrodynamic DySA are also discussed.