Metal-organic frameworks (MOFs), formed by the self-assembly of metal centres or clusters and organic linkers, possess many key structural and chemical features that have enabled them to be used in sensing platforms for a variety of environmentally, chemically and biomedically relevant compounds. In particular, their high porosity, large surface area, tuneable chemical composition, high degree of crystallinity, and potential for post-synthetic modification for molecular recognition make MOFs promising candidates for biosensing applications. In this review, we separate our discussion of MOF biosensors into two categories: quantitative sensing, focusing specifically on luminescence-based sensors for the direct measurement of a specific analyte, and qualitative sensing, where we describe MOFs used for fluorescence microscopy and as magnetic resonance imaging contrast agents. We highlight several key publications in each of these areas, concluding that MOFs present an exciting, versatile new platform for biosensing applications and imaging, and we expect to see their usage grow as the field progresses.