We present a new set of stellar interior and synthesis models for predicting the integrated emission from stellar populations in star clusters and galaxies of arbitrary age and metallicity. This work differs from existing spectral synthesis codes in a number of important ways, namely (1) the incorporation of new stellar evolutionary tracks, with sufficient resolution in mass to sample rapid stages of stellar evolution; (2) a physically consistent treatment of evolution in the Hertzsprung-Russell (HR) diagram, including the approach to the main sequence and the effects of mass loss on the giant and horizontal branch phases. Unlike several existing models, ours yield consistent ages when used to date a coeval stellar population from a wide range of spectral features and colour indexes. We use Hipparcos data to support the validity of our new evolutionary tracks. We rigorously discuss degeneracies in the age-metallicity plane and show that inclusion of spectral features blueward of 4500 Angstrom suffices to break any remaining degeneracy and that with moderate S/N spectra (10 per 20-Angstrom resolution element) age and metallicity are not degenerate. We also study sources of systematic errors in deriving the age of a single stellar population and conclude that they are not larger than 10-15 per cent. We illustrate the use of single stellar populations by predicting the colours of primordial protogalaxies and show that one can first find them and then deduce the form of the initial mass function (IMF) for the early generation of stars in the Universe. Finally, we provide accurate analytic fitting formulae for ultrafast computation of colours of single stellar populations.