We make a detailed investigation of the properties of Lyman-break galaxies (LBGs) in the ΛCDM model. We present predictions for two published variants of the galform semi-analytical model: the Baugh et al. model, which has star formation at high redshifts dominated by merger-driven starbursts with a top-heavy initial mass function (IMF), and the Bower et al. (2006) model, which has active galactic nuclei (AGN) feedback and a standard solar neighbourhood IMF throughout. We show predictions for the evolution of the rest-frame far-UV luminosity function in the redshift range z= 3–20, and compare with the observed luminosity functions of LBGs at z= 3–10. We find that the Baugh et al. model is in excellent agreement with these observations, while the Bower et al. model predicts too many high-luminosity LBGs. Dust extinction, which is predicted self-consistently based on galaxy gas contents, metallicities and sizes, is found to have a large effect on LBG luminosities. We compare predictions for the size evolution of LBGs at different luminosities with observational data for 2 ≲z≲ 7, and find the Baugh et al. model to be in good agreement. We present predictions for stellar, halo and gas masses, star formation rates, circular velocities, bulge-to-disc ratios, gas and stellar metallicities and clustering bias, as functions of far-UV luminosity and redshift. We find a broad consistency with current observational constraints. We then present predictions for the abundance and angular sizes of LBGs out to very high redshift (z≤ 20), finding that planned deep surveys with JWST should detect objects out to z≲ 15. We predict that the effects of dust extinction on the far-UV luminosity density should be large (∼2 mag), even out to high redshifts. The typical UV luminosities of galaxies are predicted to be very low at high redshifts, which has implications for detecting the galaxies responsible for reionizing the intergalactic medium; for example, at z= 10, 50 per cent of the ionizing photons are expected to be produced by galaxies fainter than MAB(1500 Å) − 5 log h∼−15.