Porous polymer and copolymer membranes are useful for ultrafiltration of functional macromolecules, colloids, and water purification. In particular, block copolymer membranes offer a bottom-up approach to form isoporous membranes. To optimize permeability, selectivity, longevity, and cost, and to rationally design fabrication processes, direct insights into the spatiotemporal structure evolution are necessary. Because of a multitude of nonequilibrium processes in polymer membrane formation, theoretical predictions via continuum models and particle simulations remain a challenge. We compiled experimental observations and theoretical approaches for homo- and block copolymer membranes prepared by nonsolvent-induced phase separation and highlight the interplay of multiple nonequilibrium processes-evaporation, solvent-nonsolvent exchange, diffusion, hydrodynamic flow, viscoelasticity, macro- and microphase separation, and dynamic arrest-that dictates the complex structure of the membrane on different scales.