  We review recent developments in theoretical studies of galaxy formation and
evolution. In combination with new data from HST, Keck and other large
telescopes, numerical and semi-analytic modelling is beginning to build up a
coherent picture of galaxy formation. We summarize the current status of
modelling of various galactic properties such as the structure of dark matter
halos, the galaxy luminosity function, the Tully-Fisher relation, the
colour-magnitude relation for ellipticals, the gross morphological properties
of galaxies and the counts of faint galaxies as a function of magnitude,
redshift and morphology. Many of these properties can be explained, at least at
some level, within a broad class of CDM cosmologies, but a number of
fundamental issues remain unresolved. We use our semi-analytic model of galaxy
formation to interpret the evolutionary status of the Lyman-break galaxies at
$z\simeq 3-3.5$ recently discovered by Steidel et al. The abundance and global
properties of these objects are compatible with model predictions in a variety
of CDM cosmologies, including the standard version. All these models predict
mild evolution in the distribution of star formation rates which peaks at
around $z\simeq 1$, but is never much larger than it is at present. The Steidel
et al. Lyman-break galaxies are among the very first objects in which
appreciable star formation is taking place; they thus signal the onset of
galaxy formation. We present three example evolutionary histories of
Lyman-break galaxies which illustrate that these objects are the precursors of
present day, normal, bright ellipticals and spirals.
