In this paper the application of the kinetic theory to the collisionless regions of the polar and solar winds is discussed. A brief historical review is given to illustrate the evolution of the theoretical models proposed to explain the main phenomenon and observations. The parallelism between the development of the solar wind models and the evolution of the polar wind theory is stressed especially. The kinetic approaches were in both cases preceded by the hydrodynamic models, and their publication gave rise to animated controversies; later on, semikinetic and hydromagnetic approximations were introduced. A kinetic method, based on the quasi neutrality and the zero current condition in a stationary plasma with open magnetic field lines, is described. The applicability of this approach on the solar and polar winds is illustrated by comparison of the predicted results with the observations. The kinetic models are also compared with hydrodynamic ones. The validity of the criticism and remarks uttered during the Chamberlain‐Parker controversy (for the solar wind), and the dispute between Banks and Holzer on the one hand, and Dessler and Cloutier on the other (for the polar wind), are carefully analyzed. The main result of this study is that both approaches are in fact not contradictory but complementary. The classical hydrodynamic descriptions are only appropriate in the collision‐dominated region, whereas the kinetic theory can be applied only in the collision‐free domain.