AbstractThe Sun has long been considered a constant star, to the extent that its total irradiance was termed the solar constant. It required radiometers in space to detect the small variations in solar irradiance on timescales of the solar rotation and the solar cycle. A part of the difficulty is that there are no other constant natural daytime sources to which the Sun's brightness can be compared. The discovery of solar irradiance variability rekindled a long‐running discussion on how strongly the Sun affects our climate. A non‐negligible influence is suggested by correlation studies between solar variability and climate indicators. The mechanism for solar irradiance variations that fits the observations best is that magnetic features at the solar surface, i.e. sunspots, faculae and the magnetic network, are responsible for almost all variations (although on short timescales convection and p‐mode oscillations also contribute). In spite of significant progress important questions are still open. Thus there is a debate on how strongly irradiance varies on timescales of centuries (i.e. how much darker the Sun was during the Maunder minimum than it is today). It is also not clear how the solar spectrum changes over the solar cycle. Both these questions are of fundamental importance for working out just how strongly the Sun influences our climate. Another interesting question is how solar irradiance variability compares with that of other cool dwarfs, particularly now that observations from space are available also for stars. (© 2013 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)