  The history of the transition from a neutral intergalactic medium (IGM) to
one that is almost fully ionized can reveal the character of cosmological
ionizing sources and set important constraints on the stellar birthrate at high
redshifts. The hydrogen component in a highly inhomogeneous universe is
completely reionized when the number of photons emitted above 1 ryd in one
recombination time equals the mean number of hydrogen atoms. If stellar sources
are responsible for photoionizing the IGM at z=5, the rate of star formation at
this epoch must be comparable or greater than the one inferred from optical
observations of galaxies at z=3, and the mean metallicity per baryon in the
universe greater than 1/500 solar. In hierarchical clustering scenarios, high-z
dwarfs (i.e. an early generation of stars in dark matter halos with circular
velocities of order 50 km/s) are expected to be one of the main source of UV
photons and heavy elements at early epochs. They would be very numerous, >0.2
arcsec^{-2}, and faint, I_AB> 29.5 mag: their detection may have to wait for
the Next Generation Space Telescope.
