Scientists and the public were alarmed at the first large viral variant of SARS‐CoV‐2 reported in December 2020. We have followed the time course of emerging viral mutants and variants during the SARS‐CoV‐2 pandemic in ten countries on four continents. We examined > 383,500 complete SARS‐CoV‐2 nucleotide sequences in GISAID (Global Initiative of Sharing All Influenza Data) with sampling dates extending until April 05, 2021. These sequences originated from ten different countries: United Kingdom, South Africa, Brazil, United States, India, Russia, France, Spain, Germany, and China. Among the 77 to 100 novel mutations, some previously reported mutations waned and some of them increased in prevalence over time. VUI2012/01 (B.1.1.7) and 501Y.V2 (B.1.351), the so‐called UK and South Africa variants, respectively, and two variants from Brazil, 484K.V2, now called P.1 and P.2, increased in prevalence. Despite lockdowns, worldwide active replication in genetically and socio‐economically diverse populations facilitated selection of new mutations. The data on mutant and variant SARS‐CoV‐2 strains provided here comprise a global resource for easy access to the myriad mutations and variants detected to date globally. Rapidly evolving new variant and mutant strains might give rise to escape variants, capable of limiting the efficacy of vaccines, therapies, and diagnostic tests. Synopsis This 2020/21 time course study shows the rapid rise of new SARS‐CoV‐2 mutants and variants across the entire genome during worldwide viral replication. In 10 countries, 40 to 65% of mutants were C to T transitions. Viral mutations will affect vaccination programs. We analyzed > 383,500 SARS‐CoV‐2 RNA sequences for the occurrence of mutations across the entire genome. The time course of mutations emerging between 01/2020 and 03/2021 was determined. We initially identified ~ 10 prevalent mutations. About 77 to 100 new mutations arose concomitant with the spread of Covid‐19 between March/April 2020 and January 2021, followed by the emergence of variants in December 2020. A study of the pathogenicity of viral mutations will help understand Covid‐19 outbreaks and symptoms. Monitoring mutant selection will aid Covid‐19 diagnosis, vaccine development and therapy. New mutants will compromise vaccine efficiency. Among the SARS‐CoV‐2 mutants, C to U transitions at a frequency between 40 to 65% were prevalent. Cellular cytosine deaminases, possibly of the APOBEC type, likely drive viral mutagenesis. This 2020/21 time course study shows the rapid rise of new SARS‐CoV‐2 mutants and variants across the entire genome during worldwide viral replication. In 10 countries, 40 to 65% of mutants were C to T transitions. Viral mutations will affect vaccination programs.