In this chapter, the correlated sampling technique, for Monte Carlo eigenvalue perturbation calculations, is described. Several issues that lead to the combination of the fission matrix and correlated sampling methods as a Monte Carlo eigenvalue perturbation technique are discussed. The idea of performing a Monte Carlo simulation in an artificial reference system, different from both the unperturbed and perturbed systems, is introduced. Numerical results are provided in support of all the theories developed in this chapter.