BCS theory of conventional superconductivity is based on pairing of each electron state with its exact time reverse, resulting in a coherent condensate of spin singlet pairs, which is insensitive to non-magnetic scattering (Anderson theorem). Such superconductors are characterized by an order parameter which breaks U(1)-gauge symmetry leading to the basic properties, such as the Meissner effect, persistent current and flux quantization. By contrast, unconventional superconductors exhibit additional broken symmetries, which lead often to distinctive superconducting phases with unique properties including sensitivity to non-magnetic scattering. Of particular interest to us is the case of time reversal symmetry breaking (TRSB) which involves magnetism and is predicted to exhibit some anomalous properties. In this talk we will review our recent studies of TRSB in several systems including the triplet superconductor Sr2RuO4, the pseudogap state of high temperature superconductors, and the inverse proximity effect in superconductor/ferromagnet bilayer structures.