Among the various uncertainties present in climate modeling, the variability of total solar irradiance is not one of the least. For lack of any direct measure of the solar irradiance in the past, substitutes are needed. However, the difficulties are twofold: (1) the reliability of the proxies and (2) the need for some physical mechanism relating these proxies to the solar luminosity. On the basis of a better understanding of the solar machinery we can now propose a plausible scenario connecting the exchanges of energy between the various reservoirs: magnetic, thermal, gravitational, and kinetic. In the present paper we discuss the available proxies and suggest a way to reconstruct total solar irradiance over the past four centuries. The response of the Laboratoire de M¿t¿orologie Dynamique atmospheric general circulation model to magnetoconvective solar forcing during the Maunder minimum is discussed. The simulated cooling appears to be compatible with temperature data from the Little Ice Age; in addition, it is found that variations of globally homogeneous external forcing parameters, like incoming solar flux or greenhouse gas loading, yield climate responses with very similar geographical patterns. ¿ American Geophysical Union 1993