The untangling or overwinding of genetic material is an inevitable part of DNA replication, repair, recombination, and transcription. Topoisomerases belong to a conserved enzyme family that amends DNA topology during various processes of DNA metabolism. To relax the genetic material, topoisomerases transiently break the phosphodiester bond on one or both DNA strands and remain associated with the cleavage site by forming a covalent enzyme–DNA intermediate. This releases torsional stress and allows the broken DNA to be re-ligated by the enzyme. The biological function of topoisomerases ranges from the separation of sister chromatids following DNA replication to the aiding of chromosome condensation and segregation during mitosis. Topoisomerases are also actively involved in meiotic recombination. The unicellular apicomplexan parasite, Plasmodium falciparum, harbors different topoisomerase subtypes, some of which have substantially different sequences and functions from their human counterparts. This review highlights the biological function of each identified Plasmodium topoisomerase along with a comparative analysis of their orthologs in human or other model organisms. There is also a focus on recent advancements towards the development of topoisomerase chemical inhibitors, underscoring the druggability of unique topoisomerase subunits that are absent in humans. Plasmodium harbors three distinct genomes in the nucleus, apicoplast, and mitochondria, respectively, and undergoes non-canonical cell division during the schizont stage of development. This review emphasizes the specific developmental stages of Plasmodium on which future topoisomerase research should focus.