Self-organized spatiotemporal patterns are crucial for the function of organisms on all levels, from intracellular molecular organization to developing embryos. A central problem in understanding the formation of intracellular protein patterns is the coupling between the membrane surface and the cytosolic bulk. This bulk-surface coupling is a fundamental and general property of protein-based pattern formation, where proteins undergo attachment and detachment at the cell membrane. However, the consequences of this bulk-surface coupling remain poorly understood. We have developed a systematic theoretical understanding of pattern formation in a concrete bulk-surface coupled system, namely the Min system of E. coli - a paradigmatic model system for studying biological pattern formation in vivo and in vitro. Our theoretical findings, in combination with experiments confirming the theoretical predictions, have allowed us to finally solve a long-standing puzzle, namely the qualitative differences between in vivo pole-to-pole oscillations and in vitro waves of Min proteins.