Parasites of the genus Leishmania cause a variety of devastating and often fatal diseases in humans worldwide. Because a vaccine is not available and the currently small number of existing drugs are less than ideal due to lack of specificity and emerging drug resistance, the need for new therapeutic strategies is urgent. Natural products and their derivatives are being used and explored as therapeutics and interest in developing such products as antileishmanials is high. The enzyme arginase, the first enzyme of the polyamine biosynthetic pathway in Leishmania, has emerged as a potential therapeutic target. The flavonols quercetin and fisetin, green tea flavanols such as catechin (C), epicatechin (EC), epicatechin gallate (ECG), and epigallocatechin-3-gallate (EGCG), and cinnamic acid derivates such as caffeic acid inhibit the leishmanial enzyme and modulate the host’s immune response toward parasite defense while showing little toxicity to the host. Quercetin, EGCG, gallic acid, caffeic acid, and rosmarinic acid have proven to be effective against Leishmania in rodent infectivity studies. Here, we review research on these natural products with a focus on their promise for the development of treatment strategies as well as unique structural and pharmacokinetic/pharmacodynamic features of the most promising agents.