Parity-time-reversal symmetry (PT symmetry), a symmetry for the combined operations of space inversion (P) and time reversal (T ), is a fundamental concept of physics and characterizes the functionality of materials as well as P and T symmetries. In particular, the PT -symmetric systems can be found in the centrosymmetric crystals undergoing the parity-violating magnetic order which we call the odd-parity magnetic multipole order. While this spontaneous order leaves PT symmetry intact, the simultaneous violation of P and T symmetries gives rise to various emergent responses that are qualitatively different from those allowed by the nonmagnetic P-symmetry breaking or by the ferromagnetic order. In this review, we introduce candidates hosting the intriguing spontaneous order and overview the characteristic physical responses. Various off-diagonal and/or nonreciprocal responses are identified, which are closely related to the unusual electronic structures such as hidden spin-momentum locking and asymmetric band dispersion. Contents I. Introduction II. Magnetic Parity Violation and Space-Time Symmetry A. Parity-time-reversal symmetry and parity violations B. Hidden Magnetic Degrees of Freedom in Crystals C. Multipolar degree of freedom of visible antiferromagnets III. Emergent Responses of PT -symmetric magnets A. Electric-Magnetic Classification of Response Function B. Magnetic Counterpart of Piezoelectric Effect C. Nonreciprocal Property of Electronic Transport and Optical Response 1. Nonreciprocal conductivity 2. Photocurrent generation IV. Availability of PT -symmetric Magnets and Physical Properties A. Switching the compensated magnets B. Control of electronic property with PT -symmetric magnetic order V.