Both the polar and solar winds were postulated to explain observations made before routine access to space was possible. Subsequently, significant limitations of the thermal plasma observations of the polar wind led to diverging approaches to modeling it. The hydrodynamic and kinetic approaches to modeling were able to explain the limited observational data. With no extensive and robust data set to determine the relative importance of dynamical effects in the ionosphere and convection in the magnetospheric electric field, there was no valid way to choose between the competing approaches. This has caused confusion in the space and plasma physics communities regarding the polar wind. Recent polar wind observations from the Japanese Akebono, NASA Polar, and the upcoming Canadian e-POP missions call for an appropriate and timely review of our current understanding of the polar wind. This paper presents a review of the modeling techniques from the earliest primitive approaches to the most current treatments that account for collision processes, non-Maxwellian distributions of multiple ion species, the role of photoelectrons in controlling plasma outflow and other topics. A brief overview of early polar wind measurements is given in Appendix B.