Surely the oldest of all suspected solar-terrestrial connections -- and by far the most important in terms of potential societal impacts -- are probable links between solar variations and regional or global climate. Dramatic advances in recent years in both solar physics and in climatology have moved this age-old question out of the closet and into the light of more rigorous tests and examination. They also allow us to frame it more clearly in the context of other, competing or interactive climate change mechanisms. For the Sun, these advances include, among others, the results from a quarter century of radiometric monitoring of solar irradiance from space; the exploitation of naturally-sequestered cosmogenic isotope records to extend the known history of solar activity hundreds of thousands of years into the past; and success in defining the impacts of variations in solar ultraviolet radiation on stratospheric chemistry and dynamics. Similar seminal advances in what we know of climate and climatic change include vast improvements in our knowledge of the interactive climate system and in our ability to model and test possible forcing mechanisms; and the recovery and accumulation of longer and more extensive records of environmental changes of the past. We shall summarize the outstanding questions that today limit what we know or think we know about the Sun-climate connection, and what needs to be done to answer them.