Understanding the formation and evolution of the first stars and galaxies represents one of the most exciting frontiers in astronomy. Since the universe was filled with hydrogen atoms at early times, the most promising probe of the epoch of the first stars is the prominent 21-cm spectral line of hydrogen. Current observational efforts are focused on the cosmic reionization era, but observations of the pre-reionization cosmic dawn are also promising. While observationally unexplored, theoretical studies predict a rich variety of observational signatures from cosmic dawn. As the first stars formed, their radiation (plus that from stellar remnants) produced significant cosmic events including Lyman-alpha coupling at z~25, and early X-ray heating. Much focus has gone to studying the angle-averaged power spectrum of 21-cm fluctuations. Additional probes include the global (sky-averaged) 21-cm spectrum, and the line-of-sight anisotropy of the 21-cm power spectrum. A particularly striking signature may result from the recently recognized effect of a supersonic relative velocity between the dark matter and gas. Work in this field, focused on understanding the whole era of reionization and cosmic dawn with analytical models and numerical simulations, is likely to grow in intensity and importance, as the theoretical predictions are finally expected to confront 21-cm observations in the coming years. [Abridged]
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