Emerging viral infections of the nervous system represent a major global public health concern in the 21st century. They are caused primarily by RNA viruses and are mostly associated with acute or subacute encephalitis. The spectrum of associated central or peripheral nervous system disorders is broad, and results either from a direct viral effect or due to the host immune responses against the infection. Emerging viral infections impose substantial neurological morbidity and mortality, particularly in low- and middle-income regions. In the past five decades, vector-borne viruses primarily transmitted by arthropods, or arboviruses, have been responsible for epidemics with a high burden of neurological disease, like the 2015-2016 Zika virus epidemic in the Americas. Viruses that have become neurovirulent for humans after geographical expansion include West Nile, Dengue, and Zika viruses. Factors such as animal migration, disruption of ecological niches, and cross-species contact have caused old viruses to reappear and cause neurological disease, as is the case of Ebola virus. In addition to these biological challenges, current preventive strategies, vaccination, and diagnostic and therapeutic approaches remain limited. We review the clinical-virological features and global impact of the most relevant emerging viral infections of the nervous system as they are projected over the 21st century.