The paper reviews the main advantages and limitations of the kinetic exospheric and fluid models of the solar wind (SW). The general theoretical background is outlined: the Boltzmann and Fokker-Planck equations, the Liouville and Vlasov equations, the plasma transport equations derived from an "equation of change". The paper provides a brief history of the solar wind modeling. It discusses the hydrostatic model imagined by Chapman, the first supersonic hydrodynamic models published by Parker and the first generation subsonic kinetic model proposed by Chamberlain. It is shown that a correct estimation of the electric field, as in the second generation kinetic exospheric models developed by Lemaire and Scherer, provides a supersonic expansion of the corona, reconciling the hydrodynamic and the kinetic approach. The modern developments are also reviewed emphasizing the characteristics of several generations of kinetic exospheric and multi-fluid models. The third generation kinetic exospheric models consider kappa velocity distribution function (VDF) instead of a Maxwellian at the exobase and in addition they treat a non-monotonic variation of the electric potential with the radial distance; the fourth generation exospheric models include Coulomb collisions based on the Fokker-Planck collision term. Multi-fluid models of the solar wind provide a coarse grained description of the system and reproduce with success the spatio-temporal variation of SW macroscopic properties (density, bulk velocity). The main categories of multi-fluid SW models are reviewed: the 5-moment, or Euler, models, originally proposed by Parker to describe the supersonic SW expansion; the 8-moment and 16-moment fluid models, the gyrotropic approach with improved collision terms as well as the gyrotropic models based on observed VDFs. The outstanding problem of collisions, including the long range Coulomb encounters, is also discussed, both in the kinetic and multi-fluid context. Although for decades the two approaches have been seen as opposed, in this paper we emphasize their complementarity. The review of the kinetic and fluid models of the solar wind contributes also to a better evaluation of the open questions still existent in SW modeling and suggests possible future developments.