Research on nanocellular foams is motivated in part by the promise of physical properties, in particular mechanical properties, that can go beyond the classical mechanical framework. However, due to the difficulty in obtaining foams of a given density but different cell sizes, determining the effect of cell size on the mechanical properties of polymer foams remains a challenge. To overcome this difficulty, studies on the mechanical behaviour of mesocellular, microcellular and nanocellular polymer foams have been compiled in this review article. After describing the different cellular structures between meso-, micro- and nanocellular foams, the mechanical properties are examined as a function of relative density and cell size. It is shown that for small strains and at low strain rates, nanocellular foams exhibit mechanical behaviour predicted by the Gibson and Ashby model. Relative density remains the first important factor to be taken into account when studying the Young’s modulus and buckling stress of nanocellular foams. The focus then shifts to fracture properties, as microcellular foams have already been shown to be far superior to more conventional foams. As studies are still scarce and different methodologies have been used, no general conclusions can be drawn. However, the fracture and impact properties could be greatly improved by this change in scale. The local confinement of molecular chains in polymeric nanocellular foams or the relaxation of the triaxial stress state in front of the crack tip could explain these observations.