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

Bound states in the continuum (BICs) defy the conventional intuition of open photonic systems by supporting perfectly localized eigenmodes within the radiative spectrum. Originally conceived in quantum mechanics and later realized in photonics, BICs have evolved from a theoretical curiosity into a unifying framework for engineering high-<i>Q</i> resonances in periodic optical structures. Unlike conventional high-<i>Q</i> 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.