We investigate the use of surface brightness fluctuations (SBF) measurements in optical and near-IR bandpasses for both stellar population and distance studies. New V-band SBF data are reported for five galaxies in the Fornax cluster and combined with literature data to define a V-band SBF distance indicator, calibrated against Cepheid distances to the Leo group and the Virgo and Fornax clusters. The colour dependence of the V-band SBF indicator is only ~15 per cent steeper than that found for the I band, and the mean `fluctuation colour' of the galaxies is ~2.4. We use new stellar population models, based on the latest Padua isochrones transformed empirically to the observational plane, to predict optical and near-IR SBF magnitudes and integrated colours for a wide range of population ages and metallicities. We examine the sensitivity of the predicted SBF-colour relations to changes in the isochrones, stellar transformations, and initial mass function. The new models reproduce fairly well the weak dependence of V and I SBF in globular clusters on metallicity, especially if the more metal-rich globulars are younger. Below solar metallicity, the near-IR SBF magnitudes depend mainly on age, while the integrated colours depend mainly on metallicity. This could prove a powerful new approach to the age-metallicity degeneracy problem; near-IR SBF observations of globular clusters would be an important test of the models. The models also help in understanding the (V-I) and (I-K) fluctuation colours of elliptical galaxies, with much less need for composite stellar populations than in previous models. However, in order to obtain theoretical calibrations of the SBF distance indicators, we combine the homogeneous population models into composite models and select out those ones with fluctuation colours consistent with observations. We are able to reproduce the observed range of elliptical galaxy (V-I) colours, the slopes of the V and I SBF distance indicators against (V-I) (fainter SBF in redder populations), and the flattening of the I-band relation for (V-I)<~1.0. The models also match the observed slope of I-band SBF against the Mg2 absorption index and explain the steep colour dependence found by Ajhar et al. for the HST/WFPC2 F814W-band SBF measurements. In contrast to previous models, ours predict that the near-IR SBF magnitudes will also continue to grow fainter for redder populations. The theoretical V-band SBF zero-point predicted by these models agrees well with the Cepheid-calibrated V-band empirical zero-point. However, the model zero-point is 0.15-0.27mag too faint in the I band and 0.24-0.36mag too faint in K. The zero-points for the I band (empirically the best determined) would come into close agreement if the Cepheid distance scale were revised to agree with the recent dynamical distance measured to NGC 4258. We note that the theoretical SBF calibrations are sensitive to the uncertain details of stellar evolution, and conclude that the empirical calibrations remain more secure. However, the sensitivity of SBF to these finer details potentially makes it a powerful, relatively unexploited, constraint for stellar evolution and population synthesis.