In this work, we study the evolution of the mass-metallicity relations (MZRs) as predicted by the GAlaxy Evolution and Assembly (gaea) semi-analytic model. We contrast these predictions with recent results from the VANDELS survey, which allows us to expand the accessible redshift range for the stellar MZR up to z similar to 3.5. We complement our study by considering the evolution of the gas-phase MZR in the same redshift range. We show that gaea is able to reproduce the observed evolution of the z < 3.5 gas-phase MZR and z < 0.7 stellar MZR, while it overpredicts the stellar metallicity at z similar to 3.5. Furthermore, gaea also reproduces the so-called fundamental metallicity relation (FMR) between gas-phase metallicity, stellar mass, and star formation rate (SFR). In particular, the gas-phase FMR in gaea is already in place at z similar to 5 and shows almost no evolution at lower redshift. gaea predicts the existence of a stellar FMR that is, however, characterized by a relevant redshift evolution, although its shape follows closely the gas-phase FMR. We also report additional unsolved tensions between model and data: the overall normalization of the predicted MZR agrees with observations only within similar to 0.1 dex; the largest discrepancies are seen at z similar to 3.5 where models tend to slightly overpredict observed metallicities; the slope of the predicted MZR at fixed SFR is too steep below a few M-circle dot yr(-1). Finally, we provide model predictions for the evolution of the MZRs at higher redshifts, which would be useful in the context of future surveys, like those that will be performed with James Webb Space Telescope.