Bound states in the continuum: From fundamental physics to emerging photonic paradigms

modes that rely on fine parameter tuning to suppress radiation, BICs arise from symmetry enforcement, destructive interference, or momentum-space topology, endowing them with intrinsic robustness and distinct design principles. This review provides a cohesive perspective on the physical origin, theoretical foundations, and emerging functionalities of BICs in photonic crystal slabs, metasurfaces, and related platforms. By bridging band theory, temporal coupled-mode theory, and multipole analysis with experimentally accessible observables, we elucidate how BIC physics enables rational control of confinement, radiation, and modal coherence. We further highlight recent advances in quasi-BIC platforms, demonstrating how controlled radiative coupling facilitates enhanced emission, nonlinear processes, and non-local wavefront manipulation. Looking forward, the integration of BIC concepts with topology-assisted design and reconfigurable photonic architectures points toward scalable, multifunctional, and intelligent photonic technologies.