Transposable elements (TEs) are ubiquitous components of eukaryotic genomes. They have considerably affected their size, structure and function. The sequencing of a multitude of eukaryote genomes has revealed some striking differences in the abundance and diversity of TEs among eukaryotes. Protists, plants, insects and vertebrates contain species with large numbers of TEs and species with small numbers, as well as species with diverse repertoires of TEs and species with a limited diversity of TEs. There is no apparent relationship between the complexity of organisms and their TE profile. The profile of TE diversity and abundance results from the interaction between the rate of transposition, the intensity of selection against new inserts, the demographic history of populations and the rate of DNA loss. Recent population genetics studies suggest that selection against new insertions, mostly caused by the ability of TEs to mediate ectopic recombination events, is limiting the fixation of TEs, but that reduction in effective population size, caused by population bottlenecks or inbreeding, significantly reduces the efficacy of selection. These results emphasize the importance of drift in shaping genomic architecture.