Various quantum mechanical effects such as nonadiabatic transition, tunneling, and interference phenomena play crucial roles in chemical and biological systems. Semiclassical molecular dynamics is an attempt to properly treat these effects in computational simulations, and this book presents and explains how this may be achieved with the use of new methods and theoretical frameworks developed by the authors. This semiclassical approach could provide a powerful step forward to tackle and clarify the quantum dynamics in large chemical and biological systems, which is currently not feasible by the full quantum mechanical methods.