Over the two years that we have been experiencing the Severe Acute Respiratory Syndrome Coronavirus-2 (SARS-CoV-2) pandemic, our challenges have been the race to develop vaccines and the difficulties in fighting against new variants due to the rapid ability of the virus to evolve. In this sense, different organizations have identified and classified the different variants that have been emerging, distinguishing between variants of concern (VOC), variants of interest (VOI), or variants under monitoring (VUM). The following review aims to describe the latest updates focusing on VOC and already de-escalated variants, as well as to describe the impact these have had on the global situation. Understanding the intrinsic properties of SARS-CoV-2 and its interaction with the immune system and vaccination is essential to make out the underlying mechanisms that have led to the appearance of these variants, helping to determine the next steps for better public management of this pandemic.