  We review recent theoretical results on the formation of the first stars and
quasars in the universe, and emphasize related open questions. In particular,
we list important differences between the star formation process at high
redshifts and in the present-day universe. We address the importance of heavy
elements in bringing about the transition from an early star formation mode
dominated by massive stars, to the familiar mode dominated by low mass stars,
at later times. We show how gamma-ray bursts can be utilized to probe the first
epoch of star formation. Finally, we discuss how the first supermassive black
holes could have formed through the direct collapse of primordial gas clouds.
