The use of immune checkpoint inhibitors (ICIs) has represented a major advance in cancer treatment. By enhancing endogenous immune responses to destroy cancer cells, ICIs can cause immune-related adverse events (irAEs), with possible involvement of any organ system. IrAEs are frequent, particularly those involving the skin or the endocrine system, and usually completely reversible after temporary immunosuppression, while neurological irAEs (n-irAEs) are relatively rare, often severe, and they carry a considerable risk of mortality and long-term disability. They usually affect the peripheral nervous system, mainly manifesting as myositis, polyradiculoneuropathy, or cranial neuropathy, and, less frequently, involve the central nervous system, causing encephalitis, meningitis, or myelitis. Although somehow reminiscent of the disorders that neurologists are familiar to deal with in their daily practice, n-irAEs are characterized by distinctive features from their idiopathic counterparts; for instance, myositis may have a predominant oculo-bulbar involvement reminiscent of myasthenia gravis and frequently associates with myocarditis; peripheral neuropathy, although often resembling Guillain-Barré syndrome, usually responds to corticosteroids. Remarkably, several associations between the neurological phenotype and the type of ICIs or the type of cancer have emerged in the last few years, and the growing administration of ICIs in patients with neuroendocrine cancers has led to an increased number of reports of paraneoplastic neurological syndromes (triggered or worsened by ICIs). This review aims to update current knowledge regarding the clinical presentation of n-irAEs. We also discuss the essential parts of the diagnostic approach, and we provide general recommendations for the management of these disorders.