Abstract
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.

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