In recent years, interstellar dust has become a crucial topic in the study of the high and very high redshift Universe. Evidence points to the existence of high dust masses in massive star forming galaxies already during the Epoch of Reionization, potentially affecting the escape of ionising photons into the intergalactic medium. Moreover, correctly estimating dust extinction at UV wavelengths is essential for precise ultra-violet luminosity function (UVLF) prediction and interpretation. In this paper, we investigate the impact of dust on the observed properties of high redshift galaxies, and cosmic reionization. To this end, we couple a physical model for dust production to the fully coupled radiation-hydrodynamics cosmological simulation code RAMSES-CUDATON, and perform a $16^3$, $2048^3$, simulation, that we call DUSTiER for DUST in the Epoch of Reionization. It yields galaxies with dust masses and UV slopes compatible with constraints at z $\geq 5$. We find that extinction has a dramatic impact on the bright end of the UVLF, even as early as $\rm z=8$, and our dusty UVLFs are in better agreement with observations than dust-less UVLFs. The fraction of obscured star formation rises up to 55% at $\rm z=5$, in agreement with some of the latest results from ALMA. Finally, we find that dust reduces the escape of ionising photons from galaxies more massive than $10^{10} M_\odot$ (brighter than $\approx -18$ MAB1600) by >10%, and possibly up to 80-90% for our most massive galaxies. Nevertheless, we find that the ionising escape fraction is first and foremost set by neutral Hydrogen in galaxies, as the latter produces transmissions up to 100 times smaller than through dust alone.