The physics of strong coupling phenomena in semiconductor quantum microcavities is reviewed. This is a relatively new field with most important developments having occurred in the last 5 years. We describe how such microcavities enable both electronic and photonic properties of semiconductors, and the interaction between them, to be controlled in the same structure. The resulting coupled exciton-photon eigenstates, cavity polaritons, have many interesting properties including very low mass for small in-plane wavevectors, and can be studied easily and directly in optical experiments, unlike exciton-polaritons in bulk semiconductors. A wealth of new optical phenomena has been reported in this field in the last few years. This review describes the most important of these phenomena. We discuss the reasons why polaritons have fundamentally different properties in microcavities as compared with those in bulk materials or quantum wells. We explain the factors which control the strength of the exciton-photon coupling and how the resulting optical spectra can be modelled. We then emphasize, in the main body of the review, the particularly important results of reflectivity experiments at both normal and oblique angles of incidence, the effects of external electric and magnetic fields, the results of coherent Raman scattering experiments, the effects of disorder on microcavity spectra, including the observation of motional narrowing over the exciton disorder potential, studies of coupled microcavities, and photoluminescence and time-resolved phenomena.