Recent evidence from ocean and ice cores suggests that a significant fraction of the variability in northern hemisphere climate since the last Ice Age correlates with solar activity [Bond et al., 2001]. This finding extends previous evidence connecting solar activity and climate during the past millennium [Eddy, 1976, Lean et al., 1995]. The simplest mechanism relies on increases of wavelength-integrated output of solar heat and light (total irradiance, S) accompanying increases in solar activity. But recent findings cast doubt on earlier evidence for a sufficiently large variation of S. At the same time, advances in instrumentation give promise of answering this question, to support timely decisions on global warming. In this article, we assess the status of the topic and suggest some new initiatives.