Topoisomerases introduce transient DNA breaks to relax supercoiled DNA, remove catenanes and enable chromosome segregation. Human cells encode six topoisomerases (TOP1, TOP1mt, TOP2α, TOP2β, TOP3α and TOP3β), which act on a broad range of DNA and RNA substrates at the nuclear and mitochondrial genomes. Their catalytic intermediates, the topoisomerase cleavage complexes (TOPcc), are therapeutic targets of various anticancer drugs. TOPcc can also form on damaged DNA during replication and transcription, and engage specific repair pathways, such as those mediated by tyrosyl-DNA phosphodiesterase 1 (TDP1) and TDP2 and by endonucleases (MRE11, XPF-ERCC1 and MUS81). Here, we review the roles of topoisomerases in mediating chromatin dynamics, transcription, replication, DNA damage repair and genomic stability, and discuss how deregulation of topoisomerases can cause neurodegenerative diseases, immune disorders and cancer.