Transposable elements (TEs) are sequences capable of multiplying in their host's genome. They survive by increasing copy numbers due to transpositions, and natural selection washes them out because hosts with heavier loads of TEs have lower fitness. The available phylogenetic evidence supports the view that TEs have existed in living organisms for hundreds of millions of years. A fundamental question facing the field is how can an equilibrium be attained between transposition and selection which allows these parasitic genetic elements to persist for such a long time period? To answer this question, it is necessary to understand how the rate of TE transposition is controlled and to describe the mechanisms with which natural selection opposes TE accumulation. Perhaps the best models for such a study are copia and gypsy retrotransposons in Drosophila. Their average rate of transposition in nature is between 10(-5) - 10(-4) transpositions per copy per generation. Unlike nature, transposition rates vary widely, from zero to 10(-2), between laboratory lines. This variability in transposition rate is controlled by host genes. It is probable that in nature TE site heterogeneity is caused by frequent transpositions in rare flies with permissive alleles, and no transpositions happen in the rest of flies. The average rate of TE transposition in nature may thus depend on the frequency of permissive alleles, which is a function of the rate of mutation from restrictive to permissive alleles, the mechanism and the strength of selection opposing TE multiplication, and population size. Thus, evolution of the frequency of permissive alleles of genes controlling transposition must be accounted for to understand evolution of TE copy numbers.