This paper highlights the role played by diffusion processes to achieve a better characterization of structure and dynamics in atomic-scale studies of materials. Two classes of examples are presented. In the first, we take advantage of diffusion coefficients to assess the performances of different exchange-correlation functionals employed within the framework of density functional theory. By calculating the diffusion coefficients one is able to make a choice on the functional best suited to describe a prototypical disordered system, liquid GeSe2. In the second class of examples, we rely on classical molecular dynamics to describe diffusion mechanism on nanostructured substrates. The migration of a Co adatom on a stepped Pt(111) surface is analyzed in detail and correlated to the value of the different diffusion barriers. The diffusion behavior of Au adatoms on the reconstructed Au(111) substrate is described in terms of diffusion isotropy and anisotropy, by comparison with the case of Co/Au(111). Taken altogether, these studies exemplify the close link between diffusion properties, a realistic description of materials and the current level of performances of atomic-scale simulations methods.