The kinetics of interfacial roughening, and its effect on the complete wetting of a substrate, are studied theoretically. Dynamical interface models are used to analyze the effects of fluctuations on the late stages of wetting for several different cases: at high temperatures (far from the roughening transition), near the roughening transition, in the presence of a random external field, as well as for the case where a local conservation law is present. The time dependence for the growth of the diffuse wetting layer which is predicted can be tested experimentally or by numerical simulation.