Diffusion on the nano/atomic scales in multilayers, thin films has many challenging features even if the role of structural defects (grain-boundaries, dislocations, etc.) can be neglected and 'only' the effects related to the nano/atomic scale raise. This can be the case for diffusion in amorphous materials, in epitaxial, highly ideal thin films, or multilayers where diffusion along short circuits can be ignored and 'only' fundamental difficulties related to nanoscale effects are important. The objective of this article is to review some interesting fundamental experimental and theoretical results in the field of nanoscale volume diffusion in planar and spherical geometries.