The research on the design of efficient, reliable, and cost-effective biosensors is expanding given its high demand in various fields such as health care, environmental surveillance, agriculture, diagnostics, industries, and so forth. In the last decade, various fascinating and interesting 2D materials with extraordinary properties have been experimentally synthesized and theoretically predicted. 2D materials have been explored for the sensing of different biomolecules because of their large surface area and strong interaction with different biomolecules. Theoretical simulations can bring important insight on the interaction of biomolecules on 2D materials, charge transfer, orbital interactions, and so forth and may play an important role in the development of efficient biosensors. Quantum simulation techniques, such as density functional theory (DFT), are very powerful and are gaining popularity especially with the advent of high-speed computing facilities. This review article provides theoretical insight regarding the interaction of various biomolecules on different 2D materials and the charge transfer between the biomolecules and 2D materials leading to electrochemical signals, which can then provide experimentalists the useful design parameters for fabrication of biosensors. It also includes an overview of quantum simulations, use of the DFT method for simulating biomolecules on 2D materials, parameters obtained from theoretical simulations and sensitivity, and limitations of computational techniques for sensing biomolecules on 2D materials. Furthermore, this review summarizes the recent work in first-principles investigation of 2D materials for the purpose of biomolecule sensing. Beyond the traditional graphene or 2D transition-metal dichalcogenides, some novel and recently proposed 2D materials such as pentagraphene, haeckelite, MXenes, and so forth which have exhibited good sensing applications have also been highlighted.