21 cm cosmology in the 21st century

Imaging the Universe during the first hundreds of millions of years remains one of the exciting challenges facing modern cosmology. Observations of the redshifted 21 cm line of atomic hydrogen offer the potential of opening a new window into this epoch. This will transform our understanding of the formation of the first stars and galaxies and of the thermal history of the Universe. A new generation of radio telescopes is being constructed for this purpose with the first results starting to trickle in. In this review, we detail the physics that governs the 21 cm signal and describe what might be learnt from upcoming observations. We also generalize our discussion to intensity mapping of other atomic and molecular lines.