DNA topology is the study of geometrical (supercoiling) and topological (knotting) properties of DNA loops and circular DNA molecules. Multiple cellular processes, such as DNA replication and transcription, affect the topology of DNA. Controlling these changes is key to ensuring stability inside the cell. Changes in DNA topology are mediated by enzymes such as topoisomerases and site-specific recombinases. We have successfully used techniques from knot theory and low-dimensional topology, aided by computational tools, to analyze the action of site-specific recombinases. I will introduce the tangle model and report on two recent analyses: 1. Based on the difference topology experimental results of Pathania, Jayaram, and Harshey (Cell, 2002), we solve 3-string tangle equations to understand the topological structure of DNA within the Mu transpososome. Pathania et al. (2002) proposed one 3-string tangle model for the Mu transpososome. We describe other families of solutions to the same tangle equations and we argue that the model given by Pathania et al. (2000) is the only biologically reasonable one. 2. The FtsK-XerCD system has been to successfully unlink complicated DNA catenanes produced by lambda Int and by DNA replication. We use tangles to argue that a stepwise unlinking by multiple recombination steps is the only plausible mechanism of action.