SARS-CoV-2 exploits angiotensin-converting enzyme 2 (ACE2) as a receptor to invade cells. It has been reported that the UK and South African strains may have higher transmission capabilities, eventually in part due to amino acid substitutions on the SARS-CoV-2 Spike protein. The pathogenicity seems modified but is still under investigation. Here we used the experimental structure of the Spike RBD domain co-crystallized with part of the ACE2 receptor, several in silico methods and numerous experimental data reported recently to analyze the possible impacts of three amino acid replacements (Spike K417N, E484K, N501Y) with regard to ACE2 binding. We found that the N501Y replacement in this region of the interface (present in both the UK and South African strains) should be favorable for the interaction with ACE2, while the K417N and E484K substitutions (South African strain) would seem neutral or even unfavorable. It is unclear if the N501Y substitution in the South African strain could counterbalance the K417N and E484K Spike replacements with regard to ACE2 binding. Our finding suggests that the UK strain should have higher affinity toward ACE2 and therefore likely increased transmissibility and possibly pathogenicity. If indeed the South African strain has a high transmission level, this could be due to the N501Y replacement and/or to substitutions in regions located outside the direct Spike–ACE2 interface but not so much to the K417N and E484K replacements. Yet, it should be noted that amino acid changes at Spike position 484 can lead to viral escape from neutralizing antibodies. Further, these amino acid substitutions do not seem to induce major structural changes in this region of the Spike protein. This structure–function study allows us to rationalize some observations made for the UK strain but raises questions for the South African strain.