Surface transport models proceeding via surface re-emission and surface diffusion are briefly described. The important dimensionless parameter for re-emission is the sticking probability, whereas for surface diffusion, profile evolution is governed by the Damkohler number. The results of our continuum-based models are presented for low pressure deposition. These transport phenomena also occur during etching, and simulation results for the evolution of surface roughness during RIE are presented. Etching of periodic surfaces is considered first. It is shown that for etching, unlike for deposition, surface roughness always decays with time; the greater the sticking probability, the greater the rate of decay. Results for etching of self-affine surfaces are presented. During deposition, it is found that the presence of surface diffusion removes sharp edges from the film profile, especially in the early stages of film growth. During RIE, on the other hand, this "cauliflower" morphology is reduced to sharper asperities, though the "peak-to-peak" roughness decays with time. This microstructnre is simulated in patterned features and is particularly important when the characteristic length scale is the same order of magnitude as the critical feature dimension. Experimental results on the evolution of roughness for a PVD process (sputter-deposition of titanium) obtained through AFM are presented, and the growth of rms roughness indicates the relative absence of surface transport.