This overview is devoted to some unresolved basic problems in crystal growth kinetics. The density wave approach to propagation of a spatially diffuse interface between a growing crystal and its simple (e.g., metallic) melt is discussed in Section 2. This approach allows for the calculation of kinetic coefficients and is an alternative to the localized interface concept in which each atom belongs to either a solid or a liquid. Sections 3 and 4 deal mainly with layer growth from solution. Mutual retardation of the growth steps via their bulk and surface diffusion fields is the major subject. The influence of solution flow on step bunching (Section 4) suggests the essential influence of bulk diffusion on the surface morphology. The flow within the solution boundary layer enhances step-step interaction, influences the step bunching process and the resulting step pattern morphology on the growing surface. Recent experiments on the rates at which strongly polygonized steps on protein and small molecule crystals propagate during growth from solution are analyzed in Section 5. We have shown that the step segments may be "singular" and that "one-dimensional nucleation" may be the rate limiting stage for the segments that are shorter or comparable in length to the thermodynamic equilibrium interkink distance. In this case, the reciprocal dependence of the segment propagation rate on the segment length that follow from the Gibbs-Thomson law, should be replaced by an abrupt switch from zero to a finite constant velocity. Until recently, the Kossel crystal remained the only model used in crystal growth theory. In such Kossel crystals, all kinks at the steps are identical and the kink rate is a linear function of the supersaturation. In the non-Kossel crystals, there may be several kink configurations characterized by different geometries and energies. These configurations should appear in a specific sequence when each new lattice unit cell is filled. As a result of such a cooperative interaction within the unit cell, a non-linear dependence of the kink rate on the vapor pressure or solution concentration in excess over the equilibrium value should be expected. (C) 2004 Elsevier B.V. All rights reserved.