Vigorous vaccination programs against SARS-CoV-2-causing Covid-19 are the major chance to fight this dreadful pandemic. The currently administered vaccines depend on adenovirus DNA vectors or on SARS-CoV-2 mRNA that might become reverse transcribed into DNA, however infrequently. In some societies, people have become sensitized against the potential short- or long-term side effects of foreign DNA being injected into humans. In my laboratory, the fate of foreign DNA in mammalian (human) cells and organisms has been investigated for many years. In this review, a summary of the results obtained will be presented. This synopsis has been put in the evolutionary context of retrotransposon insertions into pre-human genomes millions of years ago. In addition, studies on adenovirus vector-based DNA, on the fate of food-ingested DNA as well as the long-term persistence of SARS-CoV-2 RNA/DNA will be described. Actual integration of viral DNA molecules and of adenovirus vector DNA will likely be chance events whose frequency and epigenetic consequences cannot with certainty be assessed. The review also addresses problems of remaining adenoviral gene expression in adenoviral-based vectors and their role in side effects of vaccines. Eventually, it will come down to weighing the possible risks of genomic insertions of vaccine-associated foreign DNA and unknown levels of vector-carried adenoviral gene expression versus protection against the dangers of Covid-19. A decision in favor of vaccination against life-threatening disease appears prudent. Informing the public about the complexities of biology will be a reliable guide when having to reach personal decisions about vaccinations.