This chapter introduces the nonlinear polarization through a field-dependent susceptibility. It justifies this connection using a classical picture based on an anharmonic oscillator model. The connection between the polarization and fields is expanded to include more possible field couplings by treating the susceptibility as a tensor. The chapter focuses primarily on and developing a formalism for the nonlinear susceptibility for the so-called second-order effects. It focuses on one particular second-order process, the electro-optic (EO) effect, which describes one way to control the index of refraction through the nonlinear properties of a material. The chapter also covers the more general aspects of the nonlinear susceptibility. This assumption is formalized with a discussion on Kleinman's symmetry. The derivation of a nonlinear polarization given is typically used for most second-order nonlinear effects. However, the so-called linear electro-optic effect effect, also known as the Pockels' effect, uses a different formalism and a different terminology.