The study of the solar corona has been strewn with great discoveries, surpr
ises and controversies. The major steps since van de Hulst's (1953) and Cha
pman's (1957) early hydrostatic models of the extended corona, until the mo
st recent generations of kinetic models of the coronal expansion and of the
supersonic solar wind flows, are presented. These models are compared to i
n-situ 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.