At the beginning of 2021, anti-SARS-CoV-2 vaccination campaigns had been launched in almost 60 countries with more than 500 million doses having been distributed. In addition to the few vaccines already in use, many other candidates are in preclinical phases or experimental stages in humans. Despite the fact that the availability of anti-SARS-CoV-2 vaccine constitutes a major advance and appear to be the only way to control the pandemic, some investigation remains to be carried out, and this is notably concerning the impact on transmissibility, the duration of the conferred protection in the mid- and long term, the effectiveness against present and future viral mutants, or the ideal schedule that should be applied. In this paper, we review the circumstances that facilitated such a rapid development of anti-SARS-CoV-2 vaccines and summarize the different vaccine platforms under investigation as well as their present results and perspectives in different settings. We also discuss the indications of vaccination under special conditions, such as a history of previous COVID-19 infection or belonging to extreme age categories like children and elderly. Overall, this review highlights the multiple challenges to face if aiming to find a global solution to the pandemic through high vaccination coverage all over the world.