Fungal infections represent a growing public health problem, mainly stemming from two phenomena. Firstly, certain diseases (e.g., AIDS and COVID-19) have emerged that weaken the immune system, leaving patients susceptible to opportunistic pathogens. Secondly, an increasing number of pathogenic fungi are developing multi-drug resistance. Consequently, there is a need for new antifungal drugs with novel therapeutic targets, such as type I and II DNA topoisomerase enzymes of fungal organisms. This contribution summarizes the available information in the literature on the biology, topology, structural characteristics, and genes of topoisomerase (Topo) I and II enzymes in humans, two other mammals, and 29 fungi (including Basidiomycetes and Ascomycetes). The evidence of these enzymes as alternative targets for antifungal therapy is presented, as is a broad spectrum of Topo I and II inhibitors. Research has revealed the genes responsible for encoding the Topo I and II enzymes of fungal organisms and the amino acid residues and nucleotide residues at the active sites of the enzymes that are involved in the binding mode of topoisomerase inhibitors. Such residues are highly conserved. According to molecular docking studies, antifungal Topo I and II inhibitors have good affinity for the active site of the respective enzymes. The evidence presented in the current review supports the proposal of the suitability of Topo I and II enzymes as molecular targets for new antifungal drugs, which may be used in the future in combined therapies for the treatment of infections caused by fungal organisms.