This paper describes recent progress in high field magnetism mainly done in the Research Centre for Extreme Materials, Osaka University, with a short survey of the history. The main activities are concentrated on the condensed matter physics covering the field of magnetism and superconductivity where a common keyword is ’highly correlated electron physics’. A wide range of studies of metamagnetism, field-induced electronic transitions under high field, is summarised. These high field states are regarded as field-induced quantum states with various novel properties. High field is also effective for various atomic and molecular sciences. Nonlinear Zeeman effect, field-induced transparency and diamagnetic orientation of organic and biological materials are shown as examples. New frontiers in the high field technologies are shown with a highly sensitive magnetometer using the dynamical Faraday effect.