Gene assembly in stichotrichous ciliates happening during sexual reproduction is one of the most involved DNA manipulation processes occurring in biology. This biological process is of high interest from the computational and mathematical points of view due to its close analogy with such concepts and notions in theoretical computer science as permutation and linked list sorting and string rewriting. Studies on computational properties of gene assembly in ciliates represent a good example of interdisciplinary research contributing to both computer science and biology. We review here a number of general results related both to the development of different computational methods enhancing our understanding on the nature of gene assembly, as well as to the development of new biologically motivated computational and mathematical models and paradigms. Those paradigms contribute in particular to combinatorics, formal languages and computability theories.