Tandemly repeated sequences are ubiquitous components of both prokaryotic and eukaryotic genomes. Renowned examples of tandem repeats (TR) include micro-satellites, mini-satellites, or satellite DNA, as well as tandemly repeated genes. The evolutionary event that giveq rise to tandem repeats, tandem duplication, is major force that drives the formation of gene families and the evolution of the genome shape. The remarkable feature of some tandem repeats is their polymorphism: the number of copies evolve through tandem duplication or contraction that add or remove copies to the array. The polymorphism can also modify the arrangements of the variants of the repeat along the array by interleaving point mutations and duplications. This variability has dramatic effects when the TR is included in a gene or in its regulation region, as exemplified by the triplet-repeat neurodegenerative diseases in human or some diseases induced by minisatellite. In population genetics, tandem repeats polymorphism made them extremly useful markers to detect genetic variations between species, inside a population, or even between individuals for the most polymorphic ones. In this talk, we will consider two problematics in the analysis of these sequences: first, the search for tandem repeats in genomes, and second, the comparison of tandem repeat alleles to understand their evolution. We will describre algorithmical solutions for these questions and present their applications in the analysis of the evolution of the Mouse genome, as well as of a large plant specific protein family.