The World Health Organization (WHO) monitors the spread of diseases globally and maintains a list of diseases with epidemic or pandemic potential. Currently listed diseases include Chikungunya, cholera, Crimean-Congo hemorrhagic fever, Ebola virus disease, Hendra virus infection, influenza, Lassa fever, Marburg virus disease, Neisseria meningitis, MERS-CoV, monkeypox, Nipah virus infection, novel coronavirus (COVID-19), plague, Rift Valley fever, SARS, smallpox, tularemia, yellow fever, and Zika virus disease. The associated pathogens are increasingly important on the global stage. The majority of these diseases have neurological manifestations. Those with less frequent neurological manifestations may also have important consequences. This is highlighted now in particular through the ongoing COVID-19 pandemic and reinforces that pathogens with the potential to spread rapidly and widely, in spite of concerted global efforts, may affect the nervous system. We searched the scientific literature, dating from 1934 to August 2020, to compile data on the cause, epidemiology, clinical presentation, neuroimaging features, and treatment of each of the diseases of epidemic or pandemic potential as viewed through a neurologist’s lens. We included articles with an abstract or full text in English in this topical and scoping review. Diseases with epidemic and pandemic potential can be spread directly from human to human, animal to human, via mosquitoes or other insects, or via environmental contamination. Manifestations include central neurologic conditions (meningitis, encephalitis, intraparenchymal hemorrhage, seizures), peripheral and cranial nerve syndromes (sensory neuropathy, sensorineural hearing loss, ophthalmoplegia), post-infectious syndromes (acute inflammatory polyneuropathy), and congenital syndromes (fetal microcephaly), among others. Some diseases have not been well-characterized from a neurological standpoint, but all have at least scattered case reports of neurological features. Some of the diseases have curative treatments available while in other cases, supportive care remains the only management option. Regardless of the pathogen, prompt, and aggressive measures to control the spread of these agents are the most important factors in lowering the overall morbidity and mortality they can cause.