Repeated elements can be widely abundant in eukaryotic genomes, composing more than 50% of the human genome, for example. It is possible to classify repeated sequences into two large families, "tandem repeats" and "dispersed repeats." Each of these two families can be itself divided into subfamilies. Dispersed repeats contain transposons, tRNA genes, and gene paralogues, whereas tandem repeats contain gene tandems, ribosomal DNA repeat arrays, and satellite DNA, itself subdivided into satellites, minisatellites, and microsatellites. Remarkably, the molecular mechanisms that create and propagate dispersed and tandem repeats are specific to each class and usually do not overlap. In the present review, we have chosen in the first section to describe the nature and distribution of dispersed and tandem repeats in eukaryotic genomes in the light of complete (or nearly complete) available genome sequences. In the second part, we focus on the molecular mechanisms responsible for the fast evolution of two specific classes of tandem repeats: minisatellites and microsatellites. Given that a growing number of human neurological disorders involve the expansion of a particular class of microsatellites, called trinucleotide repeats, a large part of the recent experimental work on microsatellites has focused on these particular repeats, and thus we also review the current knowledge in this area. Finally, we propose a unified definition for mini- and microsatellites that takes into account their biological properties and try to point out new directions that should be explored in a near future on our road to understanding the genetics of repeated sequences.