SARS-CoV-2 is continually evolving, with more contagious mutations spreading rapidly. Using in vitro evolution to affinity maturate the receptor-binding domain (RBD) of the spike protein towards ACE2 resulted in the more contagious mutations, S477N, E484K, and N501Y, to be among the first selected, explaining the convergent evolution of the “European” (20E-EU1), “British” (501.V1),”South African” (501.V2), and Brazilian variants (501.V3). Plotting the binding affinity to ACE2 of all RBD mutations against their incidence in the population shows a strong correlation between the two. Further in vitro evolution enhancing binding by 600-fold provides guidelines towards potentially new evolving mutations with even higher infectivity. For example, Q498R epistatic to N501Y. Nevertheless, the high-affinity RBD is also an efficient drug, inhibiting SARS-CoV-2 infection. The 2.9Å Cryo-EM structure of the high-affinity complex, including all rapidly spreading mutations, provides a structural basis for future drug and vaccine development and for in silico evaluation of known antibodies.