Low-dimensional van der Waals (vdW) materials can harness tightly confined polaritonic waves to deliver unique advantages for nanophotonic biosensing. The reduced dimensionality of vdW materials, as in the case of two-dimensional graphene, can greatly enhance plasmonic field confinement, boosting sensitivity and efficiency compared to conventional nanophotonic devices that rely on surface plasmon resonance in metallic films. Furthermore, the reduction of dielectric screening in vdW materials enables electrostatic tunability of different polariton modes, including plasmons, excitons, and phonons. One-dimensional vdW materials, particularly single-walled carbon nanotubes, possess unique form factors with confined excitons to enable single-molecule detection as well as in vivo biosensing. We discuss basic sensing principles based on vdW materials, followed by technological challenges such as surface chemistry, integration, and toxicity. Finally, we highlight progress in harnessing vdW materials to demonstrate new sensing functionalities that are difficult to perform with conventional metal/dielectric sensors.