Site-specific recombinases mediate DNA recombination at sites that are directly or inversely repeated. We model circular DNA as knots or links. In this context, site-specific recombination is modeled as band surgery, a topological operation that transforms a knot into a new knot or link. We will discuss the differences in this model when the sites are directly or inversely repeated, and mention some recent work in the latter case. In particular, we prove some topological obstructions to the existence of non-coherent band surgeries relating pairs of knots. This work is joint with Vazquez.