Simulation of coexisting phases (e.g. liquid coexisting with saturated vapor, or an A-rich phase coexisting with a B-rich phase in a binary AB polymer mixture, etc.) is of interest as a tool for both the study of bulk phase properties and of interfacial properties (interfacial width, interfacial tension, etc.). Likewise, analogous experimental techniques are useful in thin film geometries. This paper reviews recent work on interfaces in polymer blends, including adsorbed block copolymers as surfactants. It is emphasized that the interfacial profile and width depend sensitively on both the lateral (L) and perpendicular (D) linear dimension of the simulation box. It is shown that simulations help to understand analogous fluctuation broadening of interfacial widths in experiment. Evidence is presented that analogous phenomena occur also for anti-phase domain walls in solid ordered binary alloys.