A number of recently developed theoretical methods for the calculation of vibrational energies and wave functions are reviewed. Methods for constructing the appropriate quantum mechanical Hamilton operator are briefly described before reviewing a particular branch of theoretical methods for solving the nuclear Schrödinger equation. The main focus is on wave function methods using the vibrational self-consistent field (VSCF) as starting point, and includes vibrational configuration interaction (VCI), vibrational Møller-Plesset (VMP) theory, and vibrational coupled cluster (VCC) theory. The convergence of the different methods towards the full vibrational configuration interaction (FVCI) result is discussed. Finally, newly developed vibrational response methods for calculation of vibrational contributions to properties, energies, and transition probabilities are discussed.