Porous polymer-derived membranes are useful for applications ranging from filtration and separation technologies to energy storage and conversion. Combining block copolymer (BCP) self-assembly with the industrially scalable, non-equilibrium phase inversion technique (SNIPS) yields membranes comprising periodically ordered top surface structures supported by asymmetric, hierarchical substructures that together overcome performance tradeoffs typically faced by materials derived from equilibrium approaches. This review first reports on recent advances in understanding the top surface structural evolution of a model SNIPS-derived system during standard membrane formation. Subsequently, the application of SNIPS to multicomponent systems is described, enabling pore size modulation, chemical modification, and transformation to non-polymeric materials classes without compromising the structural features that define SNIPS membranes. Perspectives on future directions of both single-component and multicomponent membrane materials are provided. This points to a rich and fertile ground for the study of fundamental as well as applied problems using non-equilibrium-derived asymmetric porous materials with tunable chemistry, composition, and structure.