The ABO3 perovskite oxides constitute an important family of technologically important ferroelectrics whose relatively simple chemical and crystallographic structures have contributed significantly to our understanding of ferroelectricity. They readily undergo structural phase transitions involving both polar and non-polar distortions from the ideal cubic lattice. This paper focuses on the mixed perovskite system KTa1-xNbxO3, or KTN, which has turned out to be a model system. While the end members KTaO3 and KNbO3 might be expected to be similar, in reality they exhibit very different properties. Their mixed crystals, which can be grown over the whole composition range, exhibit a rich set of phenomena whose study has added greatly to our current understanding of the phase transitions and dielectric properties of these materials. Included among these phenomena are soft mode response, ferroelectric (FE)-to-relaxor (R) crossover, quantum mechanical suppression of the transition, the appearance of a quantum paraelectric state and relaxational effects associated with dipolar impurities. Each of these phenomena is discussed briefly and illustrated. Some emphasis is on the unique role of pressure in elucidating the physics involved.