Parasitic infections are diseases transmitted by parasites usually found in contaminated food, water, or insect bites. Generally classified as neglected tropical diseases, malaria and trypanosomiases are some of the most prominent parasitic diseases that cause significant loss of life annually. In 2020, an estimated 241 million malaria cases were reported, with 627,000 deaths worldwide. An estimated 6 to 7 million people are infected with Trypanosoma cruzi worldwide, whereas an estimated 1000 global cases of African human trypanosomiasis were reported in 2020. Flavanones are a group of compounds that belong to the flavonoid family and are chemically obtained by direct cyclization of chalcones. Recent pharmacological studies have demonstrated the effectiveness of plant flavanones in inhibiting the growth of the parasites responsible for malaria and trypanosomiases. The present work aims to summarize up-to-date and comprehensive literature information on plant flavanones with antimalarial and antitrypanosomal activities. The mechanisms of action of the antiparasitic flavanones are also discussed. A literature search was performed for naturally occurring flavanones and antimalarial and antitrypanosomal activities by referencing textbooks and scientific databases (SciFinder, Wiley, American Chemical Society, Science Direct, National Library of Medicine, Scientific Electronic Library Online, Web of Science, etc.) from their inception until April 2022. Based on in vitro experiments, more than sixty flavanones were reported to exhibit antimalarial, anti-T. cruzi, and anti-T. brucei activities. Previous studies demonstrated that these compounds bind to PGP-like transporters of P. falciparum to reverse the parasite’s resistance. Other reports pinpointed the direct effect of these compounds on the mitochondria of the malaria parasite. Moreover, flavanones have shown strong docking to several validated T. cruzi and T. brucei protein targets, including adenosine kinase, pteridine reductase 1, dihydrofolate reductase, and trypanothione reductase, among others. Flavanones, isolated and characterized from diverse plant parts, were reported to exhibit moderate to high activity against P. falciparum, T. cruzi, and T. brucei in in vitro studies. These potentially active flavanones can be used as scaffolds for the development of new antiparasitic agents. However, more studies on the cytotoxicity, pharmacokinetics, and mechanisms of action of potent flavanones should be performed.