  I review recent progress in understanding the formation of the first stars
and quasars. The initial conditions for their emergence are given by the now
firmly established model of cosmological structure formation. Numerical
simulations of the collapse and fragmentation of primordial gas indicate that
the first stars formed at redshifts z ~ 20 - 30, and that they were
predominantly very massive, with M_* > 100 M_sun. Important uncertainties,
however, remain. Paramount among them is the accretion process, which builds up
the final stellar mass by incorporating part of the diffuse, dust-free envelope
into the central protostellar core. The first quasars, on the other hand, are
predicted to have formed later on, at z ~ 10, in more massive dark matter
halos, with total masses, ~ 10^8 M_sun, characteristic of dwarf galaxies.
