In the last few years, the remarkable progress in our understanding of faint galaxy data made possible by the combination of HST deep imaging  and ground-based spectroscopy , ,  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 , , , . 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 , , 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''  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 , , , 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 , , . 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.