We present a review of the auxiliary field (i.e. determinantal) Quantum Monte Carlo method applied to various problems of correlated electron systems. The ground state projector method, the finite temperature approach as well as the Hirsch‐Fye impurity algorithm are described in details. It is shown how to apply those methods to a variety of models: Hubbard Hamiltonians, periodic Anderson model, Kondo lattice and impurity problems, as well as hard core bosons and the Heisenberg model. An introduction to the world‐line method with loop upgrades as well as an appendix on the Monte Carlo method is provided. © 2003 American Institute of Physics