We describe recent continuous wave studies of stimulated polariton scattering in semiconductor microcavities, with emphasis on the variety of new physics which has been observed in the last few years. The ability to manipulate both exciton and photon properties, and how they interact together to form strongly coupled exciton-photon coupled modes, exciton polaritons, leads to a number of novel phenomena, previously unreported in bulk semiconductors or quantum wells. The unusual dispersion of the lower polariton branch, which allows energy and momentum conserving polariton-polariton parametric scattering under resonant excitation, is shown to be a key factor enabling much of the new physics. A classical theoretical treatment of the phenomena which draws parallels between the equivalent pictures of stimulated polariton scattering and those of a triply resonant optical parametric oscillator is discussed. Higher order parametric phenomena and the factors which control the threshold for stimulation are also described. The results obtained under resonant excitation are contrasted with phenomena which occur under conditions of non-resonant excitation. Prospects to achieve 'polariton lasing' under non-resonant excitation are discussed.