During evolution, several types of sequences pass through genomes. Along with mutations and internal genetic tinkering, they are a useful source of genetic variability for adaptation and evolution. Most of these sequences are acquired by horizontal transfers (HT), but some of them may come from the genomes themselves. If they are not lost or eliminated quickly, they can be tamed, domesticated, or even exapted. Each of these processes results from a series of events, depending on the interactions between these sequences and the host genomes, but also on environmental constraints, through their impact on individuals or population fitness. After a brief reminder of the characteristics of each of these states (taming, domestication, exaptation), the evolutionary trajectories of these new or acquired sequences will be presented and discussed, emphasizing that they are not totally independent insofar as the first can constitute a step towards the second, and the second is another step towards the third.