The application of BNT162b2 and mRNA-1273 vaccines against SARS-CoV-2 infection has constituted a determinant resource to control the COVID-19 pandemic. Since the beginning of 2021, millions of doses have been administered in several countries of North and South America and Europe. Many studies have confirmed the efficacy of these vaccines in a wide range of ages and in vulnerable groups of people against COVID-19. Nevertheless, the emergence and selection of new variants have led to a progressive decay in vaccine efficacy. Pfizer–BioNTech and Moderna developed updated bivalent vaccines—Comirnaty and Spikevax—to improve responses against the SARS-CoV-2 Omicron variants. Frequent booster doses with monovalent or bivalent mRNA vaccines, the emergence of some rare but serious adverse events and the activation of T-helper 17 responses suggest the need for improved mRNA vaccine formulations or the use of other types of vaccines. In this review, we discuss the advantages and limitations of mRNA vaccines targeting SARS-CoV-2 focusing on the most recent, related publications.