Phage Mu is the most efficient transposable element known, its high efficiency being conferred by an enhancer DNA element. Transposition is the end result of a series of well choreographed steps that juxtapose the enhancer and the two Mu ends within a nucleoprotein complex called the 'transpososome.' The particular arrangement of DNA and protein components lends extraordinary stability to the transpososome and regulates the frequency, precision, directionality, and mechanism of transposition. The structure of the transpososome, therefore, holds the key to understanding all of these attributes, and ultimately to explaining the runaway genetic success of transposable elements throughout the biological world. This review focuses on the path of the DNA within the Mu transpososome, as uncovered by recent topological analyses. It discusses why Mu topology cannot be analyzed by standard methods, and how knowledge of the geometry of site alignment during Flp and Cre site-specific recombination was harnessed to design a new methodology called 'difference topology.' This methodology has also revealed the order and dynamics of association of the three interacting DNA sites, as well as the role of the enhancer in assembly of the Mu transpososome.