Abstract: In recent years a great deal of work has been done on understanding quantum theories which have a non-Hermitian Hamiltonian, but which nevertheless possess a real energy spectrum, due in many cases to an underlying PT symmetry. In some circumstances, however, this symmetry may be broken, in which case some or all of the eigenvalues coalesce into complex conjugate pairs. These ideas have now found practical application in the field of classical optics, where the paraxial equation of propagation is formally identical to the Schroedinger equation, with the role of the quantum potential being played by the variations in the refractive index. Wave guides and optical lattices with the carefully coordinated regions of loss and gain implied by PT symmetry have many remarkable properties, some of which may prove useful in optical devices needed for optical computers. We review both the original concepts of PT symmetry in quantum mechanics and their application in classical optics.