This review examines different stages of the coalescence process of liquid drops on a planar interface under different conditions. Depending on the application, drops coalescence under the influence of applied external shear stress. The focus of this review is on the effect of the viscous stress, Marangoni stress, and electric field stress on the outcome of this process, particularly on the time of coalescence and partial coalescence. Theoretical progress and experiments of this phenomenon are examined, and a future outlook of this area of research is given.