International audienceWe use state-of-the-art measurements of the galaxy luminosity function (LF) at z=6, 7, and 8 to derive constraints on warm dark matter (WDM), late-forming dark matter, and ultralight axion dark matter models alternative to the cold dark matter (CDM) paradigm. To this purpose, we have run a suite of high-resolution N-body simulations to accurately characterize the low-mass end of the halo mass function and derive dark matter (DM) model predictions of the high-z luminosity function. In order to convert halo masses into UV magnitudes, we introduce an empirical approach based on halo abundance matching, which allows us to model the LF in terms of the amplitude and scatter of the ensemble average star formation rate halo mass relation, ⟨SFR(Mh,z)⟩, of each DM model. We find that, independent of the DM scenario, the average SFR at fixed halo mass increases from z=6 to 8, while the scatter remains constant. At halo mass Mh≳1012 M⊙  h−1, the average SFR as a function of halo mass follows a double power law trend that is common to all models, while differences occur at smaller masses. In particular, we find that models with a suppressed low-mass halo abundance exhibit higher SFR compared to the CDM results. Thus, different DM models predict a different faint-end slope of the LF which causes the goodness of fit to vary within each DM scenario for different model parameters. Using deviance statistics, we obtain a lower limit on the WDM thermal relic particle mass, mWDM≳1.5  keV at 2σ. In the case of LFDM models, the phase transition redshift parameter is bounded to zt≳8×105 at 2σ. We find ultralight axion dark matter best-fit models with axion mass ma≳1.6×10-22  eV to be well within 2σ of the deviance statistics. We remark that measurements at z=6 slightly favor a flattening of the LF at faint UV magnitudes. This tends to prefer some of the non-CDM models in our simulation suite, although not at a statistically significant level to distinguish them from CDM