In the past decades, nanophotonic biosensors have been extended from the extensively studied plasmonic platforms to dielectric metasurfaces. Instead of plasmonic resonance, dielectric metasurfaces are based on Mie resonance, which provide comparable sensitivity with superior resonance bandwidth, Q factor, and figure-of-merit. Although the plasmonic photothermal effect is beneficial in many biomedical applications, it is a fundamental limitation for biosensing. Dielectric metasurfaces solve the Ohmic loss and heating problems, providing better repeatability, stability, and bio-compatibility. We review the high-Q resonances based on various physical phenomena tailored by meta-atom geometric designs, and compare dielectric and plasmonic metasurfaces in refractometric, surface-enhanced, and chirality sensing for various biomedical and diagnostic applications. Departing from conventional spectral shift measurement using spectrometers, imaging-based and spectrometer-less biosensing are highlighted, including single-wavelength refractometric barcoding, surface-enhanced molecular fingerprinting, and integrated visual reporting. These unique modalities enabled by dielectric metasurfaces point to two important research directions. On the one hand, hyperspectral imaging provides massive information for smart data processing, which not only achieve better biomolecular sensing performance than conventional ensemble averaging, but also enable real-time monitoring of cellular or microbial behaviour in physiological conditions. On the other hand, a single metasurface can integrate both functions of sensing and optical output engineering, using single-wavelength or broadband light sources, which provides simple, fast, compact and cost-effective solutions. Finally, we provide perspectives in future development on metasurface materials, configurations, nanofabrication, surface modification and system integration, towards next-generation optical biosensing for ultra-sensitive, portable/wearable, lab-on-a-chip, point-of-care, multiplexed and scalable applications.