Diffusion is one of the most basic and elemental transport processes and is responsible for the molecular mixing of different chemical species. For a protein molecule, the diffusivity is given by the familiar Stokes-Einstein formula relating the Brownian diffusivity to the thermal energy times the hydrodynamic mobility of the protein: D=kT/6 \pi \eta a, where \eta is the viscosity of the solvent and a is the protein size. The Brownian self-diffusivity decreases as the concentration of protein molecules increases owing to the crowding effect of near neighbors. As the diffusing species increases in size from a protein to a several micron-sized colloidal particle, the stirring of the background fluid can give rise to another mechanism of transport – ‘shear-induced’ diffusion. Here, hydrodynamic interactions among particles promote mixing and the self-diffusivity now scales as \gamma a² , where \gamma is the shear rate. In this regime, the self-diffusivity is an increasing function of concentration since particle-particle ‘collisions’ are responsible for the diffusion motion. At still large particle size (millimeter or larger), the inertia of the particles becomes important, direct particle-particle collisions dominate the transport as opposed to the stirring of the background fluid, and the self-diffusivity now behaves like that in a dense gas: D ~ a Tg^1/2 , where Tg is the ‘granular temperature’, which is set by the stirring motion and the energy dissipated upon particle-particle collision. As in a dense gas, the self-diffusivity now decreases with increasing particle concentration. The physical origin of these various behaviors and their implications for mixing and concentration distributions in flows will be discussed.