This paper presents an overview of the main advances in the Key Questions identified by the Task Group ‘What is the Solar Influence on Climate’ by the SCOSTEP CAWSES-II science program. We go through different aspects of solar forcing from solar irradiance, including total solar irradiance (TSI) and solar spectral irradiance (SSI), to energetic particle forcing, including energetic particle precipitation (EPP) and cosmic rays (CR). Besides discussing the main advances in the timeframe 2009 to 2013, we also illustrate the proposed mechanism for climate variability for the different solar variability sources listed above. The key questions are as follows: What is the importance of spectral variations to solar influences on climate? What is the effect of energetic particle forcing on the whole atmosphere and what are the implications for climate? How well do models reproduce and predict solar irradiance and energetic particle influences on the atmosphere and climate?