The applications of REBaCuO superconducting bulks (RE: rare earth element or Y) have been investigated recently because of the enhancement of the superconducting characteristics such as critical current density Jc and the trapped field BT. A superconducting bulk can trap higher BT of over 17 T via conventional field-cooled magnetization (FCM) and BT=5.2 T via pulsed field magnetization (PFM), which has been intensively studied because a superconducting magnet is not used. This review article summarizes the magnetizing mechanism of the superconductors, the recent activities of PFM conducted experimentally and numerically, and the practical applications of several superconducting bulk magnet devices.