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 , \sim 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 \sim 1 \times 10 ^ { 9 } h ^ { -1 } M _ { \odot } and host halo masses \sim 3 \times 10 ^ { 11 } h ^ { -1 } M _ { \odot } , 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 \sim 1 \times 10 ^ { 7 } h ^ { -1 } M _ { \odot } and host halo masses \sim 2 \times 10 ^ { 10 } h ^ { -1 } M _ { \odot } , and to be generally bulge-dominated . Bright LBGs at z = 3 evolve to present-day galaxies with median stellar mass \sim 5 \times 10 ^ { 10 } h ^ { -1 } M _ { \odot } ( comparable to the Milky Way ) , consisting of roughly equal numbers of disk- and bulge-dominated systems , and hosted by halos with median mass \sim 2 \times 10 ^ { 13 } h ^ { -1 } M _ { \odot } ( 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 \sim 1 \% of bright LBGs are also predicted to also be bright SMGs ( with an 850 \mu m flux in excess of 5 mJy ) .