Since the outbreak of coronavirus disease 2019 (Covid-19) in December 2019, caused by the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2), the number of confirmed infections has risen to more than 242 million worldwide, with nearly 5 million deaths. Currently, nine Covid-19 vaccine candidates based on the original Wuhan-Hu-1 strain are at the forefront of vaccine research. All nine had an efficacy over 50% against symptomatic Covid-19 disease: NVX-CoV2373 (∼96%), BNT162b2 (∼95%), mRNA-1273 (∼94%), Sputnik V (∼92%), AZD1222 (∼81%), BBIBP-CorV (∼79%), Covaxin (∼78%), Ad26.CoV.S (∼66%) and CoronaVac (∼51%). However, vaccine efficacy (VE) can be jeopardised by the rapid emergence and spread of SARS-CoV-2 variants of concern (VOCs) that could escape from neutralising antibodies and/or cell-mediated immunity. Rare adverse events have also been reported soon after administration of viral vector and mRNA vaccines. Although many Covid-19 vaccines have been developed, additional effective vaccines are still needed to meet the global demand. Promising Covid-19 vaccines such as WIBP-CorV, AD5-nCOV, ZyCoV-D, CVnCoV, EpiVacCorona and ZF2001 have advanced to clinical studies. This review describes the most relevant mutations in the SARS-CoV-2 spike protein, discusses VE against VOCs, presents rare adverse events after Covid-19 vaccination and introduces some promising Covid-19 vaccine candidates.