Although transposable elements (TEs) have been found in all organisms in which they have been looked for, the ways in which they invade genomes and populations are still a matter of debate. By extending the classical models of population genetics, several approaches have been developed to account for the dynamics of TEs, especially in Drosophila melanogaster . While the formalism of these models is based on simplifications, they enable us to understand better how TEs invade genomes, as a result of multiple evolutionary forces including duplication, deletion, self-regulation, natural selection and genetic drift. The aim of this paper is to review the assumptions and the predictions of these different models by highlighting the importance of the specific characteristics of both the TEs and the hosts, and the host/TE relationships. Then, perspectives in this domain will be discussed.