Over the past decade, topology has emerged as a major branch in broad areas of physics, from atomic lattices to condensed matter. In particular, topology has received significant attention in photonics because light waves can serve as a platform to investigate nontrivial bulk and edge physics with the aid of carefully engineered photonic crystals and metamaterials. Simultaneously, photonics provides enriched physics that arises from spin-1 vectorial electromagnetic fields. Here, we review recent progress in the growing field of topological photonics in three parts. The first part is dedicated to the basics of topological band theory and introduces various two-dimensional topological phases. The second part reviews three-dimensional topological phases and numerous approaches to achieve them in photonics. Last, we present recently emerging fields in topological photonics that have not yet been reviewed. This part includes topological degeneracies in nonzero dimensions, unidirectional Maxwellian spin waves, higher-order photonic topological phases, and stacking of photonic crystals to attain layer pseudospin. In addition to the various approaches for realizing photonic topological phases, we also discuss the interaction between light and topological matter and the efforts towards practical applications of topological photonics.

在过去的十年中，拓扑学已成为从原子晶格到凝聚态物质等广泛物理学领域的一个主要分支。特别是，拓扑在光子学领域受到了极大的关注，因为光波可以作为一个平台，借助精心设计的光子晶体和超材料来研究重要的体和边缘物理。同时，光子学提供了由自旋 1 矢量电磁场产生的丰富物理学。在这里，我们分三个部分回顾了拓扑光子学不断发展的领域的最新进展。第一部分致力于拓扑带理论的基础知识并介绍各种二维拓扑相。第二部分回顾了三维拓扑相以及在光子学中实现它们的多种方法。最后，我们介绍了拓扑光子学中最近新兴的尚未经过审查的领域。这部分包括非零维度的拓扑简并、单向麦克斯韦自旋波、高阶光子拓扑相以及光子晶体的堆叠以获得层赝自旋。除了实现光子拓扑相的各种方法之外，我们还讨论了光与拓扑物质之间的相互作用以及拓扑光子学实际应用的努力。