  The first generation of stars, often called Population III (or Pop III), form
from metal-free primordial gas at redshifts 30 and below. They dominate the
cosmic star formation history until redshifts 15 to 20, at which point the
formation of metal-enriched Pop II stars takes over. We review current
theoretical models for the formation, properties and impact of Pop III stars,
and discuss existing and future observational constraints. Key takeaways from
this review include the following: (1) Primordial gas is highly susceptible to
fragmentation and Pop III stars form as members of small clusters with a
logarithmically flat mass function. (2) Feedback from massive Pop III stars
plays a central role in regulating subsequent star formation, but major
uncertainties remain regarding its immediate impact. (3) In extreme conditions,
supermassive Pop III stars can form, reaching masses of several 10^5 Msun.
Their remnants may be the seeds of the supermassive black holes observed in
high-redshift quasars. (4) Direct observations of Pop III stars in the early
Universe remain extremely challenging. Indirect constraints from the global
21cm signal or gravitational waves are more promising. (5) Stellar
archeological surveys allow us to constrain both the low-mass and the high-mass
ends of the Pop III mass distribution. Observations suggest that most massive
Pop III stars end their lives as core-collapse supernovae rather than as
pair-instability supernovae.
