This report combines a series of papers to trace progression in the area of type-2 topoisomerase research. First, Deibler et al. show that knotted DNA is harmful to cells. Knots can block both transcription and replication, and can also act as a catalyst for mutation. Despite the fact that type-2 topoisomerases perform the important functions of unknotting and decatenating DNA, the mechanism by which they accomplish this task is still unknown. Buck and Zechiedrich propose a model in which the enzyme uses local geometry to infer global topology, and thus where to perform segment passage in order to obtain the desired results. In two articles, Liu et al. evaluate this theory quantitatively for the decatenation and unknotting problems. In both cases it is shown that the presence of certain juxtapositions is strongly correlated with global topology. This correlation is not enough, however, and Liu et al. go on to show that when segment passage operations designed to mimic type-2 topoisomerase action are performed at hooked juxtapositions, the overwhelming tendency is towards unknotting and decatenation. / text