In the years since the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) pandemic began and spread across the globe, lessons have been learned about the challenges and opportunities that a pandemic brings to humankind. Researchers have produced many vaccines at unprecedented speed to protect people, but they have also been cognizant of the challenges presented by a new and unexpected infectious disease. The scope of this review is to examine the path of vaccine discovery so far and identify potential targets. Here, we provide insight into the leading vaccines and their advantages and challenges. We discuss the emerging mutations within the SARS-CoV-2 spike protein and other issues that need to be addressed to overcome coronavirus disease 2019 (COVID-19) completely. Future research is needed to develop a cheap, temperature-stable vaccine providing long-term immunity that protects the upper respiratory tract.