Messenger RNA (mRNA) vaccines against COVID-19 are the first authorized biological preparations developed using this platform. During the pandemic, their administration has been proven to be a life-saving intervention. Here, we review the main advantages of using mRNA vaccines, identify further technological challenges to be met during the development of the mRNA platform, and provide an update on the clinical progress on leading mRNA vaccine candidates against different viruses that include influenza viruses, human immunodeficiency virus 1, respiratory syncytial virus, Nipah virus, Zika virus, human cytomegalovirus, and Epstein-Barr virus. The prospects and challenges of manufacturing mRNA vaccines in low-income countries are also discussed. The ongoing interest and research in mRNA technology are likely to overcome some existing challenges for this technology (e.g., related to storage conditions and immunogenicity of some components of lipid nanoparticles) and enhance the portfolio of vaccines against diseases for which classical formulations are already authorized. It may also open novel pathways of protection against infections and their consequences for which no safe and efficient immunization methods are currently available.