Diffusion on the nano/atomic scales in multilayers, thin films has many challenging features even if the role of structural defects can be neglected and ‘only’ the effects related to the nano/atomic scale raise. Different examples for diffusional nanoscale effects we have discovered recently will be summarized in this paper. We illustrate that the continuum descriptions of the diffusion cannot be applied automatically on such short distances, the classical continuum approximations (Fick's laws) cannot describe correctly the atomic movements. [1-4] They predict faster kinetics than the atomistic models and the interface shift is always proportional to the squareroot of the time (x ∝ t1/2 ⇒ x2 ∝ t: parabolic or Fickian kinetics). However, the kinetics can be even linear (x ∝ t) on the nano/atomic scale. [3, 4] Furthermore, the continuum descriptions foretell infinitely fast kinetics as the time goes to zero (v=dx/dt∝1/t1/2), which is a long standing paradox of the diffusion theory. Very recently a possible resolution of this paradox has been offered , moreover, it was also shown that an initially diffused interface can sharpen even in completely miscible systems. [6, 7] We will also review the possible stress effects on the above phenomena.