Neglected tropical diseases transmitted by trypanosomatids include three major human scourges that globally affect the world’s poorest people: African trypanosomiasis or sleeping sickness, American trypanosomiasis or Chagas disease and different types of leishmaniasis. Different metabolic pathways have been targeted to find antitrypanosomatid drugs, including polyamine metabolism. Since their discovery, the naturally occurring polyamines, putrescine, spermidine and spermine, have been considered important metabolites involved in cell growth. With a complex metabolism involving biosynthesis, catabolism and interconversion, the synthesis of putrescine and spermidine was targeted by thousands of compounds in an effort to produce cell growth blockade in tumor and infectious processes with limited success. However, the discovery of eflornithine (DFMO) as a curative drug against sleeping sickness encouraged researchers to develop new molecules against these diseases. Polyamine synthesis inhibitors have also provided insight into the peculiarities of this pathway between the host and the parasite, and also among different trypanosomatid species, thus allowing the search for new specific chemical entities aimed to treat these diseases and leading to the investigation of target-based scaffolds. The main molecular targets include the enzymes involved in polyamine biosynthesis (ornithine decarboxylase, S-adenosylmethionine decarboxylase and spermidine synthase), enzymes participating in their uptake from the environment, and the enzymes involved in the redox balance of the parasite. In this review, we summarize the research behind polyamine-based treatments, the current trends, and the main challenges in this field.