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Indices of solar activity relevant for understanding and modelling solar irradiance variability are identified, and their temporal characteristics compared. Reproducing observed solar irradiance variability requires a minimum of two different types of indices — an index for irradiance depletion by sunspots and an index for global irradiance enhancement by faculae and network. When combined with appropriate wavelength-dependent parameterizations of sunspot and facular contrasts and center-to-limb functions, these indices permit the construction of empirical models of daily, monthly and annual solar total and spectral irradiances. The models are compared with observations at selected wavelengths and for the total irradiance. While the models replicate much of the rotational and 11-year cycle variance in contemporary irradiance databases, differences exist because of either the presence of variability mechanisms additional to solar magnetism, or of unresolved instrumental effects in the databases. The reconstruction of solar irradiance in the past requires speculation about the extent of intercycle fluctuations in the global facular index, or in other, as yet unspecified, variability mechanisms.