The variation of total solar irradiance (TSI) has been measured since 1978 and that of the spectral irradiance for an even shorter amount of time. Semi-empirical models are now available that reproduce over 80% of the measured irradiance variations. An extension of these models into the more distant past is needed in order to serve as input to climate simulations. Here we review our most recent efforts to model solar total and spectral irradiance on time scales from days to centuries and even longer. Solar spectral irradiance has been reconstructed since 1947. Reconstruction of solar total irradiance goes back to 1610 and suggests a value of about 1-1.5 Wm$^{-2}$ for the increase in the cycle-averaged TSI since the end of the Maunder minimum, which is significantly lower than previously assumed but agrees with other modern models. First steps have also been made towards reconstructions of solar total and spectral irradiance on time scales of millennia.
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