The literature relevant to how solar variability influences climate is vast—but much has been based on inadequate statistics and non-robust procedures. The common pitfalls are outlined in this review. The best estimates of the solar influence on the global mean air surface temperature show relatively small effects, compared with the response to anthropogenic changes (and broadly in line with their respective radiative forcings). However, the situation is more interesting when one looks at regional and season variations around the global means. In particular, recent research indicates that winters in Eurasia may have some dependence on the Sun, with more cold winters occurring when the solar activity is low. Advances in modelling “top-down” mechanisms, whereby stratospheric changes influence the underlying troposphere, offer promising explanations of the observed phenomena. In contrast, the suggested modulation of low-altitude clouds by galactic cosmic rays provides an increasingly inadequate explanation of observations.