The COVID-19 pandemic has endangered world health and the economy. As the number of cases is increasing, different companies have started developing potential vaccines using both traditional and nano-based platforms to overcome the pandemic. Several countries have approved a few vaccine candidates for emergency use authorization (EUA), showing significant effectiveness and inducing a robust immune response. Oxford-AstraZeneca, Pfizer-BioNTech’s BNT162, Moderna’s mRNA-1273, Sinovac’s CoronaVac, Johnson & Johnson, Sputnik-V, and Sinopharm’s vaccine candidates are leading the race. However, the SARS-CoV-2 is constantly mutating, making the vaccines less effective, possibly by escaping immune response for some variants. Besides, some EUA vaccines have been reported to induce rare side effects such as blood clots, cardiac injury, anaphylaxis, and some neurological effects. Although the COVID-19 vaccine candidates promise to overcome the pandemic, a more significant and clear understanding is needed. In this review, we brief about the clinical trial of some leading candidates, their effectiveness, and their neutralizing effect on SARS-CoV-2 variants. Further, we have discussed the rare side effects, different traditional and nano-based platforms to understand the scope of future development.