Label-free optical biosensing holds great promise for a variety of applications in biomedical diagnostics, environmental and food safety, and security. It is already used as a key tool in the investigation of biomolecular binding events and reaction constants in real time and offers further potential additional functionalities and low-cost designs. However, the sensitivity of this technology does not match the routinely used but expensive and slow labelling methods. Therefore, label-free optical biosensing remains predominantly a research tool. Here we discuss how one can go beyond the limits of detection provided by standard optical biosensing platforms and achieve a sensitivity of label-free biosensing that is superior to labelling methods. To this end we review newly emerging optical implementations that overcome current sensitivity barriers by employing novel structural architectures, artificial materials (metamaterials and hetero-metastructures) and using phase of light as a sensing parameter. Furthermore, we elucidate the mechanism of plasmonic phase biosensing and review hyper-sensitive transducers, which can achieve detection limits at the single molecule level (less than 1 fg mm-2) and make it possible to detect analytes at several orders of magnitude lower concentrations than so far reported in literature. We finally discuss newly emerging layouts based on dielectric nanomaterials, bound states in continuum, and exceptional points.