Frustration in magnetic materials arising from competing exchange interactions can prevent the system from adopting long-range magnetic order and can instead lead to a diverse range of novel quantum and topological states with exotic quasiparticle excitations. Here, we review prominent examples of such states, including magnetically-disordered and extensively degenerate spin ices with emergent magnetic monopole excitations, highly-entangled quantum spin liquids with fractional spinon excitations, topological order, and emergent gauge fields, as well as complex particle-like topological spin textures known as skyrmions. We provide an overview of recent advances in the search for magnetically-disordered candidate materials on the three-dimensional pyrochlore lattice and two-dimensional triangular, kagome and honeycomb lattices, the latter with bond-dependent Kitaev interactions, and on lattices supporting topological magnetism. We highlight experimental signatures of these often elusive phenomena and single out the most suitable experimental techniques that can be used to detect them. Our review also aims at providing a comprehensive guide for designing and investigating novel frustrated magnetic materials, with the potential of addressing some important open questions in contemporary condensed matter physics.

磁性材料中因竞争性交换相互作用而产生的挫败可能会阻止系统采用长程磁序，反而会导致具有奇异准粒子激发的各种新颖的量子和拓扑状态。在这里，我们回顾了此类状态的突出例子，包括具有涌现磁单极子激发的磁无序和广泛简并的自旋冰，具有分数自旋子激发的高度纠缠的量子自旋液体，拓扑序和涌现规范场，以及复杂的粒子-就像被称为斯格明子的拓扑自旋纹理一样。我们概述了在三维烧绿石晶格和二维三角形、kagome 和蜂窝​​晶格（后者具有键依赖性 Kitaev 相互作用）以及支持拓扑磁性的晶格上寻找磁无序候选材料的最新进展。我们强调这些经常难以捉摸的现象的实验特征，并挑选出可用于检测它们的最合适的实验技术。我们的综述还旨在为设计和研究新型受挫磁性材料提供全面的指南，并有可能解决当代凝聚态物理学中的一些重要的开放性问题。