An introduction to and a survey of quantum para- and ferro-electric behavior in oxide perovskites are given. In the paraelectric case, quantum fluctuations stabilize the disordered state with a high, temperature-independent dielectric constant. Application of uniaxial stress or ion substitution can induce a quantum ferroelectric state at a special quantum multicritical point (QMCP). The occurrence of or crossover to a random-field induced domain state in partially substituted crystals is reviewed. The emphasis is on SrTiO3 studies and on Sr1-xCaxTiO3 mixed crystals, but contact is made to stressed KTaO3 and substitution of K+ or Ta5+ ions. © 1985 The Japan Society of Applied Physics.