The theory of the electro-optic effect and second harmonic generation is developed in the context of the linear Stark effect. This leads to an emphasis both on the optical bandwidth of the charge-transfer transitions responsible for the hyperpolarisability, and on the relationship between the transition energies and optical frequency of an electro-optic device. A simple treatment of vibronic coupling illustrates the connection between the bond-length alternation in conjugated polyenes and the sign and magnitude of the non-linearity. A brief survey is made of current chemical strategies for optimising the non-linearity.