The outbreak of COVID-19 started in December 2019 and spread rapidly all over the world. It became clear that the development of an effective vaccine was the only way to stop the pandemic. It was the first time in the history of infectious diseases that the process of the development of a new vaccine was conducted on such a large scale and accelerated so rapidly. At the end of 2020, the first COVID-19 vaccines were approved for marketing. At the end of March 2023, over three years after the outbreak of the COVID-19 pandemic, 199 vaccines were in pre-clinical development and 183 in clinical development. The candidate vaccines in the clinical phase are based on the following platforms: protein subunit, DNA, RNA, non-replication viral vector, replicating viral vector, inactivated virus, virus-like particles, live attenuated virus, replicating viral vector combined with an antigen-presenting cell, non-replication viral vector combined with an antigen-presenting cell, and bacterial antigen-spore expression vector. Some of the new vaccine platforms have been approved for the first time for human application. This review presents COVID-19 vaccines currently available in the world, procedures for assurance of the quality and safety of the vaccines, the vaccinated population, as well as future perspectives for the new vaccine platforms in drug and therapy development for infectious and non-infectious diseases.