The SARS-CoV-2 virus is rapidly evolving via mutagenesis, lengthening the pandemic, and threatening the public health. Until August 2021, 12 variants of SARS-CoV-2 named as variants of concern (VOC; Alpha to Delta) or variants of interest (VOI; Epsilon to Mu), with significant impact on transmissibility, morbidity, possible reinfection and mortality, have been identified. The VOC Delta (B.1.617.2) of Indian origin is now the dominant and the most contagious variant worldwide as it provokes a strong binding to the human ACE2 receptor, increases transmissibility and manifests considerable immune escape strategies after natural infection or vaccination. Although the development and administration of SARS-CoV-2 vaccines, based on different technologies (mRNA, adenovirus carrier, recombinant protein, etc.), are very promising for the control of the pandemic, their effectiveness and neutralizing activity against VOCs varies significantly. In this review, we describe the most significant circulating variants of SARS-CoV-2, and the known effectiveness of currently available vaccines against them.