An overview and detailed analysis of the classical theory of capillarity is presented. A number of known equations of capillary rise dynamics are shown to be different limiting cases of one rather general equation. Some internal inconsistencies of the classical equations are pointed out, The role of nonlinear dissipation and flow pattern effects in the front zone of the liquid column and near the capillary entrance is discussed. Numerical simulations and experimental data demonstrating some characteristic types of dynamic behavior predicted by the theory are reported. Special attention is paid to the capillary rise of surfactant solutions. As applied to this special case, the existing theory is substantially elaborated by setting up a closed system of equations describing the surfactant transport and relaxation processes in the adsorption layer. A simplified relation for the capillary rise dynamics in the case of strong depletion of the interfacial region is obtained, which is in qualitative agreement with the experimental behavior.