In the last few years, the remarkable progress in our understanding of faint
galaxy data made possible by the combination of HST deep imaging
[58]
and ground-based spectroscopy
[31],
[11],
[52] has
permitted to shed some light on the evolution of the stellar birthrate in the
universe, to tentatively identify the epoch 1 
z 2 where most of
the optical extragalactic background light was produced, and to set important
contraints on galaxy evolution scenarios
[35],
[53],
[2],
[19]. The
explosion in the quantity of information available on the high-redshift
universe at optical wavelengths has been complemented by the detection of
the far-IR/sub-mm background by DIRBE and FIRAS
[24],
[12],
that has revelead the optically ``hidden'' side of galaxy formation, and
shown that a significant fraction of the energy released by stellar
nucleosynthesis is re-emitted as thermal radiation by dust. The underlying
goal of all these efforts is to understand the growth of cosmic structures
and the mechanisms that shaped the Hubble sequence, and ultimately to map
the transition from the cosmic ``dark age''
[45] to a ionized
universe populated with luminous sources. While one of the important
questions recently emerged is the nature (starbursts or AGNs?) and redshift
distribution of the ultraluminous sub-mm sources discovered by SCUBA
[27],
[1],
[32],
of perhaps equal interest is the
possible existence of a large population of faint galaxies still undetected
at high-z, as the color-selected ground-based and Hubble Deep
Field
(HDF) samples include only the brightest and bluest star-forming objects.
In hierarchical clustering cosmogonies,
high-z dwarfs and/or mini-quasars (i.e. an early generation of
stars and accreting black holes in dark matter halos with circular
velocities vc ~
50 km s-1) may actually be one of the main source of UV photons and
heavy elements at early epochs
[38],
[21],
[22]. In this
talk I will focus on some of the open issues and controversies
surrounding our present understanding of the history of the conversion of
cold gas into stars within galaxies, and of the evolution with cosmic time
of the space density of luminous sources. An Einstein-de Sitter universe
(q0 = 0.5) with
H0 = 50h50 km s-1
Mpc-1 will be adopted in the following.