Evolutionary population synthesis models for a wide range of metallicities, ages, star formation histories, initial mass functions and horizontal branch morphologies, including blue morphologies at high metallicity, are computed. The model output comprises spectral energy distributions, colours, stellar M/L ratios, bolometric corrections and near-infrared (IR) spectral line indices. The energetics of the post main sequence evolutionary phases are evaluated with the fuel consumption theorem. The impact on the models of the stellar evolutionary tracks (in particular with and without overshooting) is assessed. We find modest differences in synthetic broad-band colours as induced by the use of different tracks in our code [e.g. Δ(V−K) ∼ 0.08 mag, Δ(B−V) ∼ 0.03 mag]. Noticeably, these differences are substantially smaller than the scatter among other models in the literature, even when the latter adopt the same evolutionary tracks. The models are calibrated with globular cluster data from the Milky Way for old ages, and the Magellanic clouds plus the merger remnant galaxy NGC 7252, both for young ages of ∼0.1–2 Gyr, in a large wavelength range from the U band to the K band. Particular emphasis is put on the contribution from the thermally pulsing asymptotic giant branch (TP-AGB) phase. We show that this evolutionary phase is crucial for the modelling of young stellar populations by direct comparison with observed spectral energy distributions of Magellanic cloud clusters, which are characterized by relatively high fluxes, both blueward and redward of the V band. We find that the combination of the near-IR spectral indices C₂ and H₂O can be used to determine the metallicity of ∼1 Gyr stellar populations. As an illustrative application, we re-analyse the spectral energy distributions of some of the high-z galaxies (2.4 ≲z≲ 2.9) observed with the Spitzer Space Telescope by Yan et al. Their high rest-frame near-IR fluxes is reproduced very well with the models including TP-AGB stars for ages in the range ∼0.6–1.5 Gyr, suggesting formation redshifts for these objects around z∼ 3–6.