During May 10-11, 2024, Solar Active Region (AR) 13664 experienced one of the most intense solar storm events since the Carrington Event of 1859, triggering a G5-level geomagnetic storm (Dst index reaching -412 nT) and global auroral displays. AR 13664 exhibited a dense and complex magnetic field distribution, accompanied by rapid magnetic field evolution and high activity such as abundant magnetic emergence, topological restructuring, and the generation of multiple flares and coronal mass ejections (CMEs). AR 13664 may represent a typical process of energy accumulation and release in intense solar eruptions, making it an ideal subject for studying magnetic complexity, energy storage and release mechanisms, and the causes of strong solar eruptions. This paper reviews current relevant research findings, focusing on multi-band observations, magnetohydrodynamic modeling, and nonlinear force-free field extrapolations, to reveal the full chain physical processes from magnetic flux emergence to near-Earth space responses of AR 13664. The research results around AR 13664 indicate: (1) the region exhibited an extremely high rate of magnetic flux emergence, peaking at 2.2×10²² Mx/day, rapidly forming a complex βγδ-type magnetic structure, with a total unsigned magnetic flux of up to 1.35×10²³ Mx, laying the magnetic topological foundation for efficient energy storage; (2) magnetic topology analysis indicates that the energy release process is closely related to the evolution of quasi-separatrix layers (QSLs) and the development of multiple current sheets, revealing the energy release mechanism in local non-potential energy regions; (3) multi-stage magnetic shearing processes were clearly observed, showing the gradual formation of magnetic rope structures and enhanced instability, closely associated with subsequent eruptions of 12 X-class flares and multiple halo CMEs; (4) the associated CMEs exhibit large-scale trans-equatorial source structures and propagate swiftly through solar-terrestrial space. Some of these CMEs reach projected speeds surpassing 2000 km/s and showcase pronounced southward magnetic fields (with the North-south magnetic field Bz dropping to a minimum of -50 nT) at 1 AU. These characteristics lead to significant impacts on Earth's magnetosphere, instigating intense magnetic storms and disturbances in the ionosphere. These studies systematically depict the full chain evolution process of extreme space weather events from the solar source to near-Earth space, providing innovative insights into the triggering, energy accumulation, release, and propagation mechanisms of solar eruptions, and offering an important research foundation for establishing more accurate and predictable space weather models.