mRNA was discovered in 1961, but it was not used as a vaccine until after three decades. Recently, the development of mRNA vaccine technology gained great impetus from the pursuit of vaccines against COVID-19. To improve the properties of RNA vaccines, and primarily their circulation time, self-amplifying mRNA and trans-amplifying mRNA were developed. A separate branch of mRNA technology is circular RNA vaccines, which were developed with the discovery of the possibility of translation on their protein matrix. Circular RNA has several advantages over mRNA vaccines and is considered a fairly promising platform, as is trans-amplifying mRNA. This review presents an overview of the mRNA platform and a critical discussion of the more modern self-amplifying mRNA, trans-amplifying mRNA, and circular RNA platforms created on its basis. Finally, the main features, advantages, and disadvantages of each of the presented mRNA platforms are discussed. This discussion will facilitate the decision-making process in selecting the most appropriate platform for creating RNA vaccines against cancer or viral diseases.