We predict the formation histories, properties and descendants of Lyman-break galaxies (LBGs) in the Lambda-CDM cosmology. In our model, which incorporates a top-heavy IMF in starbursts, we find that most LBGs are starbursts triggered by minor mergers of galaxies. The duration of the LBG phase is predicted to be quite short, ~20-60 Myr. We investigate the distributions of stellar and halo masses and morphologies for bright (L_UV > L*_UV) and faint (L_UV > 0.1 L*_UV) LBGs at z=3, z=6 and z=10 (where we classify LBGs according to their rest-frame UV luminosities relative the observed characteristic luminosity L*_UV at z approx 3). Bright LBGs at z=3 are predicted to have median stellar masses ~ 1x10^9 Msun/h and host halo masses ~ 3x10^{11} Msun/h, and to be typically mildly disk-dominated in stellar mass. On the other hand, faint LBGs at z=10 are predicted to have median stellar masses of only ~ 1x10^7 Msun/h and host halo masses 2x10^{10} Msun/h, and to be generally bulge-dominated. Bright LBGs at z=3 evolve to present-day galaxies with median stellar mass ~ 5x^{10} Msun/h (comparable to the Milky Way), consisting of roughly equal numbers of disk- and bulge-dominated systems, and hosted by halos with median mass ~2x10^{13} Msun/h (corresponding to medium-size galaxy groups). The model predicts that 40% of Milky Way mass galaxies at the present-day have a bright LBG progenitor in the redshift range 3<z<4, while 95% have a faint LBG progenitor in the same redshift range, and 7% have a faint LBG progenitor at 10<z<11. With our multiwavelength model, we also investigate the overlap between the LBG population and that of submillimetre selected galaxies (SMGs); at z=3, only ~1% of bright LBGs are also predicted to also be bright SMGs (with an 850 mum flux in excess of 5 mJy).
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