Abstract: The physics of high magnetic fields is a subject rich in achievements. Steady high magnetic fields above 40T have been successfully developed, providing new opportunities for studying solid state physics under such fields. An overview is presented of recent progress in this area, including the H-T phase diagram and non-Fermi liquid behavior of high temperature superconductors, the de Haas effect and properties of the Fermi surface, Wigner crystalligation of electrons and its dynamical properties, magnetic field-induced phase transitions such as insulator-metal and superconductor transitions multistage magnetic ordering, successive spin density waves and the quantum Hall effect in bulk material.