Since the first case of Coronavirus disease (COVID-19) caused by severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) in 2019, SARS-CoV-2 infection has affected many individuals worldwide. Eventually, some highly infectious mutants—caused by frequent genetic recombination—have been reported for SARS-CoV-2 that can potentially escape from the immune responses and induce long-term immunity, linked with a high mortality rate. In addition, several reports stated that vaccines designed for the SARS-CoV-2 wild-type variant have mixed responses against the variants of concern (VOCs) and variants of interest (VOIs) in the human population. These results advocate the designing and development of a panvaccine with the potential to neutralize all the possible emerging variants of SARS-CoV-2. In this context, recent discoveries suggest the design of SARS-CoV-2 panvaccines using nanotechnology, siRNA, antibodies or CRISPR-Cas platforms. Thereof, the present comprehensive review summarizes the current vaccine design approaches against SARS-CoV-2 infection, the role of genetic mutations in the emergence of new viral variants, the efficacy of existing vaccines in limiting the infection of emerging SARS-CoV-2 variants, and efforts or challenges in designing SARS panvaccines.