This chapter provides a comprehensive introduction to theory for full quantum effects and its associated numerical methods for simulations of the realistic condensed matter systems. The discussion is organized into several areas: simulations of nuclear quantum effects (NQEs), nonadiabatic effects (NAEs), the combination of these two effects, and electron–phonon coupling. For NQEs, the basic physical picture and concept of path-integral methods is introduced, as well as numerically the most commonly used first-principles path-integral molecular dynamics and path-integral Monte Carlo methods. The calculation of NQEs on statistical and dynamical properties are introduced, and specific methods (i.e., centroid molecular dynamics (CMD) and ring-polymer molecular dynamics (RPMD) methods) are explained with discussions on their advantages and disadvantages. Then, this chapter delves into a hot topic – using first principle to calculate electron–phonon coupling with expressions based on second quantization. Some theories of both perturbative and non-perturbative treatments of electron–phonon coupling, such as the finite-difference method, the supercell-averaging method, and the effective-action theory, are explained. For simulations of NAEs, this chapter focuses on theories of potential energy surface-hopping method, Ehrenfest dynamics methods, and mixed quantum–classical dynamics methods. Joint study of NQEs and NAEs is still in its infancy, and several dynamical theories are introduced, such as the mean-field ring-polymer molecular dynamics (MF-RPMD) method. Nonadiabatic reaction rate theory is introduced. Finally, this chapter provides some perspectives on full quantum theory, listing specific aspects needed to be addressed, such as the exchange interactions between fermionic nuclei, NQEs calculations for dynamic properties, and some recent efforts for simulations of the NAEs.