Quantum tunneling is an essential issue in quantum physics. Especially, the rapid development of nanotechnology in recent years promises a lot of applications in condensed matter physics, surface science and nanodevices, which are growing interests in fundamental issues, computational techniques and potential applications of quantum tunneling. The book involves two relevant topics. One is quantum tunneling theory in condensed matter physics, including the basic concepts and methods, especially for recent developments in mesoscopic physics and computational formulation. The second part is the field electron emission theory, which covers the basic field emission concepts, the Fowler - Nordheim theory, and recent developments of the field emission theory especially in some fundamental concepts and computational formulation, such as quantum confinement effects, Dirac fermion, Luttinger liquid, carbon nanotubes, coherent emission current, quantum tunneling time problem, spin polarized field electron emission and non-equilibrium Green's function method for field electron emission. This book presents in both academic and pedagogical styles, and is as possible as self-complete to make it suitable for researchers and graduate students in condensed matter physics and vacuum nanoelectronics.