  Superconductivity and magnetism are antagonistic states of matter. The
presence of spontaneous magnetic fields inside the superconducting state is,
therefore, an intriguing phenomenon prompting extensive experimental and
theoretical research. In this review, we discuss recent experimental
discoveries of unconventional superconductors which spontaneously break
time-reversal symmetry and theoretical efforts in understanding their
properties. We discuss the main experimental probes and give an extensive
account of theoretical approaches to understand the order parameter symmetries
and the corresponding pairing mechanisms including the importance of multiple
bands.
