The development of numerous programs for the identification of mobile elements raises the issue of the founding concepts that are shared in their design. This is necessary for at least three reasons. First, the cost of designing, developing, debugging and maintaining software could present a danger of distracting biologists from their main bioanalysis tasks that require a lot of energy. Some key concepts on exact repeats are always underlying the search for genomic repeats and we recall the most important ones. All along the chapter, we try to select practical tools that may help the design of new identification pipelines. Second, the huge increase of sequence production capacities requires to use the most efficient data structures and algorithms to scale up tools in front of the data deluge. This paper provides an up-to-date glimpse on the art of string indexing and string matching. Third, there exists a growing knowledge on the architecture of mobile elements built from literature and the analysis of results generated by these pipelines. Besides data management which has led to the discovery of new families or new elements of a family, the community has an increasing need in knowledge management tools in order to compare, to validate or simply to keep trace of mobile elements models. We end the paper with first considerations on what could help the near future of such research on models.