Life implies adaptation. This is one of the fundamental principles that has permitted most living species to survive through ages in an ever-changing environment. Spontaneously occurring events have shaped also virus populations and their fitness. Thanks to their plasticity, viruses have thrived in extremely dissimilar conditions. Unsurprisingly, SARS-CoV-2, the etiological agent of COVID-19, is no exception. Thanks to an unprecedented rate of molecular tracing and sequence scrutiny, the virus was followed in all its changes and shown to evolve in such a way as to possibly determine subsequent waves of infection after the first global and massive outbreak. This review illustrates the major modifications occurred to the virus since its discovery. We describe the potential advantages that these changes conveyed as regards SARS-CoV-2 transmissibility, resistance to host innate and adaptive barriers and molecular diagnosis.