  We use a semi-analytic model of galaxy formation in hierarchical clustering
theories to interpret recent data on galaxy formation and evolution, focussing
primarily on the recently discovered population of Lyman-break galaxies at
$z\simeq 3$. For a variety of cold dark matter (CDM) cosmologies we construct
mock galaxy catalogues subject to identical selection criteria to those applied
to the real data. We find that the expected number of Lyman-break galaxies is
very sensitive to the assumed stellar initial mass function and to the
normalization of the primordial power spectrum. For reasonable choices of these
and other model parameters, it is possible to reproduce the observed abundance
of Lyman-break galaxies in CDM models with $\Omega_0=1$ and with $\Omega_0<1$.
These galaxies generally form from rare peaks at high redshift and, as a
result, their spatial distribution is strongly biased, with a typical bias
parameter, $b\simeq 4$, and a comoving correlation length, $r_0\simeq 4 \mpc$.
The typical sizes of these galaxies, $\sim 0.5\kpc$, are substantially smaller
than those of present day bright galaxies. In combination with data at lower
redshifts, the Lyman-break galaxies can be used to trace the cosmic star
formation history. Most galaxies (in our models and in the data) never
experience star formation rates in excess of a few solar masses per year. Our
models predict that even at $z=5$, the integrated star formation rate is
similar to that measured locally, although less than 1% of all the stars have
formed prior to this redshift. These galaxies mark the onset of the epoch of
galaxy formation that continues into the present day. The basic ingredients of
a consistent picture of galaxy formation may well be now in place.
