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.