The notion of non-Hermitian optics and photonics rooted in quantum mechanics and photonic systems has recently attracted considerable attention ushering in tremendous progress on theoretical foundations and photonic applications, benefiting from the flexibility of photonic platforms. In this review, we first introduce the non-Hermitian topological physics from the symmetry of matrices and complex energy spectra to the characteristics of Jordan normal forms, exceptional points, biorthogonal eigenvectors, Bloch/non-Bloch band theories, topological invariants and topological classifications. We further review diverse non-Hermitian system branches ranging from classical optics, quantum photonics to disordered systems, nonlinear dynamics and optomechanics according to various physical equivalences and experimental implementations. In particular, we include cold atoms in optical lattices in quantum photonics due to their operability at quantum regimes. Finally, we summarize recent progress and limitations in this emerging field, giving an outlook on possible future research directions in theoretical frameworks and engineering aspects.

植根于量子力学和光子系统的非厄米光学和光子学的概念最近引起了相当大的关注，得益于光子平台的灵活性，在理论基础和光子应用方面取得了巨大进展。在这篇综述中，我们首先从矩阵的对称性和复能谱的对称性，到 Jordan 范式、异常点、双正交特征向量、布洛赫/非布洛赫能带理论、拓扑不变量和拓扑分类的特征，介绍了非厄米拓扑物理。我们根据各种物理等效性和实验实现，进一步回顾了从经典光学、量子光子学到无序系统、非线性动力学和光力学的各种非厄米系统分支。特别是，我们将冷原子包括在量子光子学的光学晶格中，因为它们在量子体系中具有可操作性。最后，我们总结了这一新兴领域的最新进展和局限性，展望了未来在理论框架和工程方面可能的研究方向。