In nature, biosilicification directs the formation of elaborate amorphous silica exoskeletons that provide diatoms mechanically strong, chemically inert, non-decomposable silica armor conferring chemical and thermal stability as well as resistance to microbial attack, without changing the optical transparency or adversely effecting nutrient and waste exchange required for growth. These extraordinary silica/cell biocomposites have inspired decades of biomimetic research aimed at replication of diatoms' hierarchically organized exoskeletons, immobilization of cells or living organisms within silica matrices and coatings to protect them against harmful external stresses, genetic re-programming of cellular functions by virtue of physico-chemical confinement within silica, cellular integration into devices, and endowment of cells with non-native, abiotic properties through facile silica functionalization. In this Perspective, we focus our discussions on the development and concomitant challenges of bioinspired cell silicification ranging from "cells encapsulated within 3D silica matrices" and "cells encapsulated within 2D silica shells" to extra- and intracellular silica replication, wherein all biomolecular interfaces are encased within nanoscopic layers of amorphous silica. We highlight notable examples of advances in the science and technology of biosilicification and consider challenges to advancing the field, where we propose cellular "mineralization" with arbitrary nanoparticle exoskeletons as a generalizable means to impart limitless abiotic properties and functions to cells, and, based on the interchangeability of water and silicic acid and analogies between amorphous ice and amorphous silica, we consider "freezing" cells within amorphous silica as an alternative to cryo-preservation.