Understanding the influence of solar variability on the Earth’s climate requires knowledge of solar variability, solar-terrestrial interactions, and the mechanisms determining the response of the Earth’s climate system. We provide a summary of our current understanding in each of these three areas. Observations and mechanisms for the Sun’s variability are described, including solar irradiance variations on both decadal and centennial time scales and their relation to galactic cosmic rays. Corresponding observations of variations of the Earth’s climate on associated time scales are described, including variations in ozone, temperatures, winds, clouds, precipitation, and regional modes of variability such as the monsoons and the North Atlantic Oscillation. A discussion of the available solar and climate proxies is provided. Mechanisms proposed to explain these climate observations are described, including the effects of variations in solar irradiance and of charged particles. Finally, the contributions of solar variations to recent observations of global climate change are discussed.