A previously unstudied aspect of adsorption, compression in confined phases, is discussed. For the equilibrium of a gas on a solid surface, the strong attraction to the surface causes adsorbate molecules to attain much higher densities than those of equilibrium condensed phases. Under these conditions, adsorbate molecules repel each other and heats of adsorption vanish. Adsorption compression is a nanoscale analogue of macroscale compression of air in the gravitational field of the Earth. The difference is that nanoscale compression occurs at immeasurably higher gradients of molecular forces and compression can be extremely large. This compression causes phase transitions and allows a supercompressed state of matter that is nearly impossible to obtain at normal conditions. A statistical mechanical theory of adsorption compression is developed in the framework of the grand canonical ensemble. Simulations and experimental evidence of compressed phases on solid surfaces are discussed. The significance of this phenomenon is not limited to fundamental aspects of adsorption and capillarity; it also plays a crucial role in various applications such as heterogeneous catalysis, membrane separations, and self-assembly on surfaces.