Since the discovery of Quasars, giant magnetic flares about Kerr black holes (BHs) have drawn much attention in elucidating the mechanism of astrophysical high-energy phenomena and processes, such as quasi-periodic oscillations (QPOs), γ-ray bursts (GRBs), and outflow jets. Up to now, three kinds of flares are suggested: quasi-solar flares, cascade flares, and outflow flares. Both BH-dynamo theory in Gravitomagnetic (GM) field and force-free magnetosphere are developed in the curved 4D space-time by the manipulation of the 3+1 split of geometry (i.e., 3D in space+1D in time). We introduce first of all the disk-corona model of giant flares. Then, we describe the BH dynamo processes in the GM Field. Furthermore, we overview the magnetic topology of BH magnetosphere, helicity transfer, and the Penrose process. Finally, we provide a summary on the future work of the giant flare physics. It is predicted that the dynamics of the high-energy radiation in giant flares will be brought to light by the investigation of the general relativistic magnetohydrodynamic (GRMHD) dynamo action outside the central BHs residing in a tokamak-like cosmic magnetic field.