Variability of solar irradiance on time scales longer than a day is driven by the solar surface magnetism. Models of the irradiance variability are progressively gaining in physical realism. Using high-resolution solar magnetograms, solar irradiance variations can be modelled with great accuracy. Reconstructions of the past irradiance changes are, however, hindered by the lack and the quality of the appropriate records of the past solar magnetic activity. I will review the most recent efforts and progress in reconstructions of the solar irradiance on time scales longer than the solar cycle.
Mode of presentation: oral (Need to be confirmed by the SOC)