According to Hartree's self-consistent-field (SCF) model of the atom, the motion of each electron in the effective field of theN-1 others is governed by a one-particle Schrödinger equation. Self-consistency of the electronic charge distribution with its own electrostatic field leads to a set of coupled integrodifferential equations (Hartree equations) forNone-particle wavefunctions (atomic orbitals). The Hartree equations were subsequently shown to be precisely the conditions for optimization of an approximate wavefunction consisting of a product of atomic orbitals. An improved formalism, due to Slater and to Fock, represents the atomic wavefunction by a determinant built of atomic spin-orbitals and is thereby consistent with the Pauli principle. Application of the variational principle to a Slater determinant leads to a set ofNcoupled equations (Hartree-Fock equations), quite similar to Hartree's equations but containing, in addition, exchange interactions—an effect having no classical analog. The error inherent in the Hartree-Fock method, known as electron correlation, arises from smoothing-out of interelectronic repulsive interactions into effective Coulomb and exchange potentials. It accounts for roughly a 1% error in the total energy but is magnified in energy differences, which are more directly related to experimental quantities. A significant improvement in computational facility is achieved if the orbital functions are expanded in terms of a finite set of basis functions. The integrodifferential equations are thereby transformed into algebraic equations (Roothaan's equations) for the expansion coefficients. The analytic approach makes it possible to apply the self-consistent-field method to molecular systems. To date, SCF calculations have been carried out, in some form, for all the atoms in the periodic table and for a growing list of diatomic and polyatomic molecules.