  A growing number of superconducting materials display evidence for
spontaneous time-reversal symmetry breaking (TRSB) below their critical
transition temperatures. Precisely what this implies for the nature of the
superconducting ground state of such materials, however, is often not
straightforward to infer. We review the experimental status and survey
different theoretical mechanisms for the generation of TRSB in superconductors.
In cases where a TRSB complex combination of two superconducting order
parameter components is realized, defects, dislocations and sample edges may
generate superflow patterns that can be picked up by magnetic probes. However,
even single-component condensates that do not break time-reversal symmetry in
their pure bulk phases can also support signatures of magnetism inside the
superconducting state. This includes, for example, the generation of localized
orbital current patterns or spin-polarization near atomic-scale impurities,
twin boundaries and other defects. Signals of TRSB may also arise from a
superconductivity-enhanced Ruderman-Kittel-Kasuya-Yosida exchange coupling
between magnetic impurity moments present in the normal state. We discuss the
relevance of these different mechanisms for TRSB in light of recent experiments
on superconducting materials of current interest.
