Bound states in the continuum (BICs) exhibit theoretically infinite quality factors and resonances that have ultra-narrow line widths, offering transformative potential the field of optical biosensing. This review surveys BIC-enabled biosensors and classify them by the type of materials used: metallic, all-dielectric, and metal-dielectric hybrid. This paper fist discusses BICs and how they can be categorized. Symmetry-protected and accidental BICs (such as Fabry-Pérot and Friedrich-Wintgen BICs) are discussed, and how the asymmetry of the structure can be used to explain the sensing performance of the structure using a coupled mode theory framework. Classically defined core performance metrics, i.e., quality factor, sensitivity, full width at half maximum, and figure of merit, are elaborated. Metallic BICs take advantages of plasmonic near field enhancements for low detection limits, but are limited by Ohmic losses. All-dielectric BICs achieve ultrahigh Q factors and topological robustness from Mie resonances, and hybrid systems combine the sensitivity of plasmonics with the high quality factor (Q factor) confinement of dielectrics. A range of state-of-the-art applications range from tumor phenotyping to exosome detection. Current capabilities BIC-enabled optical biosensors and analyze their potential are also assessed. Principal challenges the principal challenges ahead are highlighted, emphasizing on machine learning based designs to assist with BICs, microfluidic on-chip integration, and biosensing with gradients. These suggested technical advancements/ideas would provide the essential features to develop the intelligent biosensing systems of the future.