Adverse reactions to the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) vaccine depict a tropism for neural structures. This narrative review was aimed to discuss published data on the spectrum of neurological side effects of SARS-CoV-2 vaccines, which were accorded emergency use authorization. The majority of the neurological manifestations of SARS-CoV-2 vaccination are usually mild, brief, self-limiting, and easily manageable. Rarely, these side effects can be of serious nature and require hospitalization. High vigilance helps in early identification and treatment of these complications leading to good outcomes. The reported incidence of neurological complications in vaccinated population is a miniscule, and the overall benefits of the vaccine outweigh the risks of side effects. However, it is crucial to conduct larger collaborative multicenter studies to prove or reject the causal association between the SARS-CoV-2 vaccines and the postvaccination neurological side effects. Herein, we have tried to summarize the various neurological manifestations related to SARS-CoV-2 vaccines published in the literature from 2021 to mid-2023.