Samarium hexaboride (SmB₆) is an example of a Kondo insulator, in which strong electron correlations cause a band gap to open. SmB₆ hosts both a bulk insulating state and a conductive surface state. Within a Fermi-liquid framework, the strongly correlated ground-state electronic structure can be mapped to a simple state resembling a topological insulator. Although uncertainties remain, many experiments provide compelling evidence that the conductive surface states have a topological origin. However, the bulk behaviour is less well understood and some experiments indicate bulk in-gap states. This has inspired the development of many theories that predict the emergence of new bulk quantum phases beyond Landau’s Fermi-liquid model. We review the current progress on understanding both the surface and the bulk states, especially the experimental evidence for each. A mystery centres on the existence of the bulk in-gap states and why they appear in some experiments but not others. Adding to the mystery is why quantum oscillations in SmB₆ appear only in magnetization but not in resistivity. We conclude by elaborating on three questions: why SmB₆ is worth studying, what can be done to move forwards and what other correlated insulators could give additional insight.

六硼化（SmB ₆）是近藤绝缘子的一个示例，其中强电子相关性导致带隙打开。SmB ₆同时具有体绝缘状态和导电表面状态。在费米-液体框架内，高度相关的基态电子结构可以映射为类似于拓扑绝缘体的简单状态。尽管不确定性仍然存在，但许多实验提供了令人信服的证据，证明导电表面态具有拓扑起源。然而，整体行为尚不为人所理解，一些实验表明整体的间隙内状态。这激发了许多理论的发展，这些理论预测了Landau的费米液体模型以外的新的体量子相的出现。我们回顾了在了解表面状态和整体状态方面的最新进展，尤其是每种状态的实验证据。一个谜团是关于大量间隙内状态的存在以及为什么它们出现在某些实验中而不是其他实验中。₆仅以磁化形式出现，而不以电阻率形式出现。最后，我们通过阐述三个问题得出结论：为什么SmB ₆值得研究，可以做些什么来推动前进，以及其他哪些相关的绝缘子可以提供更多的见解。