Static correlation (SC) is essential in describing the dissociation of a covalent bond. It is one of the main issues in this book to develop a density functional which allows to describe the SC in the bond dissociations, and the aim of this chapter is to review the methods for describing the SC in the wave-function theory and in the density-functional theory (DFT). The first section is devoted to illustrate an a priori approach to construct the wave function that realizes the SC for the simplest chemical bond at the dissociation limit. Based on the result, in Sect. 2.2, a general approach in the wave-function theory, termed multi-configuration self-consistent field (MCSCF) method, is briefly reviewed. It is well known that the realization of the SC in the DFT is quite difficult since the approximate functionals refer only to the local and semi-local properties of the system, i.e. the density and its derivatives. In Sect. 2.3, we first discuss the source of the difficulty and then provide an outline of an approach in the DFT to incorporate the SC into an explicit exchange functional. An implicit method to represent the SC within the framework of the Kohn-Sham DFT is reviewed in Sect. 2.4, where the optimized effective potential (OEP) method will be adapted to the MCSCF wave function. In this chapter, the atomic units (a.u.) are used unless otherwise stated.