Metal-organic frameworks (MOFs) are a perspective class of hybrid materials for biosensing applications. Over the past few years, numerous concepts of novel biosensitive materials and devices have been proposed and developed on their basis. The detecting capability of MOF-based sensors ranges from specific ions to various physiologically active molecules such as hormones, amino acids and related byproducts, antibiotics, etc. The operating environments may be aqueous solutions or various biological media, such as serum, blood, lymph, etc. The functional response in such biosensors is based on qualitative or quantitative changes in optical or electrical properties. Engineering of bioresponsive MOFs encompasses physical, chemical, structural, and molecular design and can be supported by theoretical modeling and computational analysis. These include a set of analyses such as the relationship between the metal and organic linkers, properties of the guest molecules, and interaction with the analyte. In this review, we outline the recent advances in design, synthesis, and computational studies of various bioresponsive MOFs, along with their functional characteristics such as sensitivity, detection speed, reusability and stability. (C) 2020 Elsevier B.V. All rights reserved.