Pursuing topological phases in natural and artificial materials is one of the central topics in modern physical science and engineering. In classical magnetic systems, spin waves (or magnons) and magnetic solitons (such as domain wall, vortex, skyrmion, etc.) represent two important excitations. Recently, the topological insulator and semimetal states in magnon- and soliton-based crystals (or metamaterials) have attracted growing attention owing to their interesting dynamics and promising applications for designing robust spintronic devices. Here, we give an overview of current progress of topological phases in structured classical magnetism. We first provide a brief introduction to spin waves and their band structure in periodic lattices. Then, we elaborate typical topological invariants and pedagogical models that are important to understand the topological nature of magnons, such as the magnon Hall effect, topological magnon insulators, Dirac (Weyl) magnon semimetals, topological magnon polarons (magnon-phonon hybrid excitations), and higher-order topological magnons. Appealing proposal of topological magnonic devices is also highlighted. We then review the collective-coordinate approach for describing the dynamics of magnetic soliton lattice. We focus on the topological properties of magnetic solitons, by theoretically analyzing the first-order topological insulating phases in low dimensional systems and higher-order topological states in breathing crystals. Finally, we discuss the experimental realization and detection of the edge states in both magnonic and solitonic crystals. We remark the challenges and future prospects before concluding this article.

在自然和人造材料中追求拓扑阶段是现代物理科学和工程学的中心主题之一。在经典的磁系统中，自旋波（或磁振子）和磁孤子（例如畴壁，涡旋，天旋子等）代表两个重要的激发。近年来，由于基于磁振子和孤子的晶体（或超材料）的拓扑绝缘体和半金属态吸引了越来越多的关注，这是由于它们有趣的动力学特性以及在设计强大的自旋电子器件方面的有前途的应用。在这里，我们概述了结构化经典磁性拓扑阶段的最新进展。我们首先简要介绍自旋波及其在周期性晶格中的能带结构。然后，我们阐述了典型的拓扑不变式和教学模型，这些模型和模型对于理解磁振子的拓扑性质非常重要，例如磁振子霍尔效应，拓扑磁振子绝缘体，狄拉克（Weyl）磁振子半金属，拓扑磁振子极化子（磁振子-声子混合激发）以及更高版本阶拓扑磁振子。拓扑结构的大型设备的吸引人的建议也被重点介绍。然后，我们回顾用于描述磁孤子晶格动力学的集体坐标方法。通过理论上分析低维系统中的一阶拓扑绝缘相和呼吸晶体中的高阶拓扑状态，我们专注于磁孤子的拓扑特性。最后，我们讨论了在强子晶体和孤子晶体中边缘状态的实验实现和检测。