SARS-CoV-2, the virus that causes COVID-19, is prone to mutations and the generation of genetic variants. Since its first outbreak in 2019, SARS-CoV-2 has continually evolved, resulting in the emergence of several lineages and variants of concern (VOC) that have gained more efficient transmission, severity, and immune evasion properties. The World Health Organization has given these variants names according to the letters of the Greek Alphabet, starting with the Alpha (B.1.1.7) variant, which emerged in 2020, followed by the Beta (B.1.351), Gamma (P.1), Delta (B.1.617.2), and Omicron (B.1.1.529) variants. This review explores the genetic variation among different VOCs of SARS-CoV-2 and how the emergence of variants made a global impact on the pandemic.