Metal–Organic Frameworks (MOFs), as a new generation of hybrid porous materials, have attracted widespread attention in the field of drug delivery in recent years. The regular crystal structure, very high specific surface area, tunable porosity, and the possibility of chemical surface modification have made these nanostructures a suitable platform for drug loading and controlled release. Compared with conventional drug delivery systems such as liposomes and polymeric nanoparticles, MOFs provide higher loading capacity and more precise structural design capability. In addition, the development of MOFs responsive to stimuli such as pH, reducing agents, enzymes, and light has enabled targeted drug release in pathological environments such as tumor microenvironments. In this article, the structure and physicochemical properties of MOFs effective in biological applications are first reviewed. Then, different loading strategies and drug release mechanisms are analyzed. Also, the applications of these systems in anticancer drug delivery, gene delivery, protein delivery, and theranostics are reviewed. Next, challenges related to biocompatibility, toxicity, biostability, and barriers to clinical translation are discussed. Finally, future perspectives in the design of smart and multifunctional MOFs for clinical applications are presented.