This paper presents recent advances in the theory of multicomponent crystal growth from gas or solution, focusing on the most common step-flow mechanisms: Burton-Cabrera-Frank, Chernov, and Gilmer-Ghez-Cabrera. Analytical expressions for the spiral crystal growth rate are presented, taking into account the properties of all species involved in the growth process. The paper also outlines theoretical approaches to consider these mechanisms in multicomponent systems, providing a foundation for future developments and exploration of previously unexplored effects. Some special cases are discussed, including the formation of nanoislands of pure components on the surface and their self-organization, the impact of applied mechanical stress on the growth rate, and the mechanisms of its influence on growth kinetics. The growth due to chemical reactions on the surface is also considered. Possible future directions for developing the theory are outlined. A brief overview of numerical approaches and software codes that are useful in theoretical studies of crystal growth is also given.