μSR study on the magnetism of high-T_c cuprates is introduced. Concretely, (1) antiferromagnetic ordered phase, (2) 1/8 anomaly and the relative stripe order of spins and holes, (3) impurity-induced magnetism, (4) magnetic-field-induced magnetism, (5) pseudogap, (6) ferromagnetism in the heavily overdoped regime, (7) undoped superconductivity in T′-type cuprates are discussed. Moreover, fundamentals of μSR measurements for the study of the magnetism are described for μSR beginners.

An overview of studies is presented on 3d electron superconductors Na_xCoO₂·yH₂O and Fe-based systems discovered after high-T_c Cu oxides. We present how the neutron inelastic scattering contributed to clarify whether the magnetic mechanism is primarily important for the occurrence of the superconductivity. We also present results of the studies on dynamical properties of their lattice systems to search alternative candidate of the superconducting pairing mechanism.

A brief overview is presented how neutron inelastic scattering method has been applied to the study on Cu oxide high-T_c superconductors. Here, we mainly show results of the measurements carried out on the YBa₂Cu₃O_6+x (Y123 system), and demonstrate how these works have presented meaningful information to identify the origin of the superconductivity and underlying unusual dynamical behaviors related to its active magnetism, which originates from the fact that the system is induced from the Mott-insulating state by doping holes (or electrons).