Local repetitions in genomes are called tandem repeats. A tandem repeat contains multiple, but slightly different copies of a repeated unit. It changes over time as the copies are altered by mutations, when additional copies are created by amplification of an existing copy, or when a copy is removed by contraction. Theses changes let tandem repeats evolve dynamically. From this statement follow two problems. TANDEM REPEAT HISTORY aims at recovering the history of amplifications and mutations that produced the tandem repeat sequence given as input. Given the tandem repeat sequences at the same genomic location in two individuals and a cost function for amplifications, contractions, and mutations, the purpose of TANDEM REPEAT ALLELE ALIGNMENT is to find an alignment of the sequences having minimal cost. We present a survey of these two problems that allow to investigate evolutionary mechanisms at work in tandem repeats.