The variability of the Sun is well established, as well as that of the Earth's climate. To what extent the two are connected, in the sense that solar variability drives climate, is the subject of considerable research and, in some cases, controversy. This volume is aimed at obtaining an overview of the current knowledge of the variability of the Sun and of the Earth's climate, and of their possible connections. It is a collection of introductory and contributed papers presented at an ISSI workshop, supplemented by a summary of the discussion sessions and a workshop, thus giving a coherent overviewwhile still conveying the lively spirit that prevailed at the workshop. The volume is intended to provide the active researcher with a status report while at the same time serving the advanced graduate student with introductory material in this field of research.