Metal-organic frameworks (MOFs) are a class of coordination polymers, consisting of metal ions or clusters linked together by chemically mutable organic groups. In contrast to zeolites and porous carbons, MOFs are constructed from a building block strategy that enables molecular level control of pore size/shape and functionality. An area of growing interest in MOF chemistry is the synthesis of MOF-based composite materials. Recent studies have shown that MOFs can be combined with biomacromolecules to generate novel biocomposites. In such materials, the MOF acts as a porous matrix that can encapsulate enzymes, oligonucleotides, or even more complex structures that are capable of replication/reproduction (i.e., viruses, bacteria, and eukaryotic cells). The synthetic approach for the preparation of these materials has been termed "biomimetic mineralization", as it mimics natural biomineralization processes that afford protective shells around living systems. In this Perspective, we focus on the preparation of MOF biocomposites that are composed of complex biological moieties such as viruses and cells and canvass the potential applications of this encapsulation strategy to cell biology and biotechnology.