This chapter shows that parametric and polariton scatttering can be attributed to the decay of pump photons into photon pairs with fractional energies. The ultimate result of the quantum theory of scattering that is compared with experiment is the probability of a transition per unit time or scattering cross-section. The chapter explores this method, which is traditional among quantum mechanicists, and utilizes it to calculate the basic energy characteristics of parametric scattering. It presents a number of approaches that feature linear and nonlinear fluctuation-dissipation theorems, as well as the kinetic equation. The chapter examines a series of "one-photon" experiments in which a single detector is used to measure the intensity of scattered light. In investigating the influence of the non-ideal nature of the pump on multiphoton processes, one may identify two extreme cases, which are called "homogenous" and "inhomogenous" broadenings of the spectrum.