The study of the solar corona has been strewn with great discoveries, surprises and controversies. The major steps since van de Hulst's (1953) and Chapman's (1957) early hydrostatic models of the extended corona, until the most recent generations of kinetic models of the coronal expansion and of the supersonic solar wind flows, are presented. These models are compared to insitu observations. Progress in polar wind models went through a somewhat similar evolution that is outlined also. The advantages and limitations of the successive brands of solar wind and polar wind models are considered.