DNA topoisomerases have an essential role in resolving topological problems that arise due to the double-helical structure of DNA. They can recognise DNA topology and catalyse diverse topological reactions by cutting and re-joining DNA ends. Type IA and IIA topoisomerases, which work by strand passage mechanisms, share catalytic domains for DNA binding and cleavage. Structural information has accumulated over the past decades, shedding light on the mechanisms of DNA cleavage and re-ligation. However, the structural rearrangements required for DNA-gate opening and strand transfer remain elusive, in particular for the type IA topoisomerases. In this review, we compare the structural similarities between the type IIA and type IA topoisomerases. The conformational changes that lead to the opening of the DNA-gate and strand passage, as well as allosteric regulation, are discussed, with a focus on the remaining questions about the mechanism of type IA topoisomerases.