In standard quantum mechanics, the Hamiltonian describing the physical system is generally Hermitian, so as to ensure that the system has real energy spectra and that the system’s evolution is unitary. In recent years, it has been found that non-Hermitian Hamiltonians with parity-time (\cal PT) symmetry also have real energy spectra, and there is a novel non-Hermitian exceptional point between \cal PT-symmetric phase and \cal PT -symmetry-broken phase, which is unique to non-Hermitian systems. Recently, people have realized \cal PT symmetric and anti-\cal PT symmetric non-Hermitian Hamiltonians in various physical systems and demonstrated novel quantum phenomena, which not only deepened our understanding of the basic laws of quantum physics, but also promoted the breakthrough of application technology. This review will introduce the basic physical principles of \cal PT symmetry and anti-\cal PT symmetry, summarize the schemes to realize \cal PT symmetry and anti-\cal PT symmetry in optical and atomic systems systematically, including the observation of \cal PT -symmetry transitions by engineering time-periodic dissipation and coupling in ultracold atoms and single trapped ion, the realization of anti-\cal PT symmetry in dissipative optical system by indirect coupling, and realizing anti-\cal PT -symmetry through fast atomic coherent transmission in flying atoms. Finally, we review the research on precision sensing using non-Hermitian exceptional points of \cal PT -symmetric systems. Near the exceptional points, the eigenfrequency splitting follows an \varepsilon ^\tfrac1N-dependence, where the \varepsilon is the perturbation and N is the order of the exceptional point. We review the \cal PT-symmetric system composed of three equidistant micro-ring cavities and enhanced sensitivity at third-order exceptional points. In addition, we also review the debate on whether exceptional-point sensors can improve the signal-to-noise ratio when considering noise, and the current development of exceptional-point sensors, which is still an open and challenging question.