Metal-organic frameworks (MOFs) as sensing materials have experienced explosive growth in recent years due to their intrinsic merits, such as structural diversity, high porosity, large surface area, extraordinary adsorption affinities, etc. Biomolecules such as DNA, protein, and vitamins play vital roles in metabolism. Moreover, the sensitive detection of biomolecules is of importance in the disease prevention and treatment. This review intends to provide an update on the recent progress in the detection of various biomolecules via MOF-based luminescent sensors. MOFs are successful in the detection of DNA, RNA, protein, and other biomolecules. MOF-based luminescent sensors function by utilizing different mechanisms, including luminescent responses of enhancement and quenching, which are defined as "turn-on" and "turn-off" responses, respectively. Then, a short comparison of the "turn-on" and "turn-off" types of sensors is also made.