Computer simulations are extremely useful tools of modern theoretical chemistry that provide fundamental understanding of molecular processes and rigorous interpretations of experiments from first principles. However, a rigorous and general method for describing the influence of quantum effects on equilibrium and dynamical properties of complex systems (e.g., those with many degrees of freedom) has yet to be established. Such an accomplishment would make a major impact in our understanding of a wide range of chemical processes, including reactions in bio-molecules where proton and electron transfer often involve quantum tunneling and coherences. In addition, a broad area of research and technology development would also benefit from these advances in computational methods, since there is currently a real need for truly convenient and powerful techniques capable of describing quantum processes in new materials.