Here we tackle a problem from biology in terms of discrete mathematics. We are interested in a complex DNA manipulation process happening in eukaryotic organisms of a subclass of ciliate species called Stichotrichia during so-called gene assembly. This process is in particular interesting since one can interpret gene assembly in ciliates as sorting of permutations. We survey here results related to studies on sorting permutations with some specific rewriting rules that formalize elementary intramolecular gene assembly operations. The research question is \what permutation may be sorted with our operations?"