Leishmaniasis is one of the major public health concerns in Latin America, Africa, Asia, and Europe. The absence of vaccines for human use and the lack of effective vector control programs make chemotherapy the main strategy to control all forms of the disease. However, the high toxicity of available drugs, limited choice of therapeutic agents, and occurrence of drug-resistant parasite strains are the main challenges related to chemotherapy. Currently, only a small number of drugs are available for leishmaniasis treatment, including pentavalent antimonials (SbV), amphotericin B and its formulations, miltefosine, paromomycin sulphate, and pentamidine isethionate. In addition to drug toxicity, therapeutic failure of leishmaniasis is a serious concern. The occurrence of drug-resistant parasites is one of the causes of therapeutic failure and is closely related to the diversity of parasites in this genus. Owing to the enormous plasticity of the genome, resistance can occur by altering different metabolic pathways, demonstrating that resistance mechanisms are multifactorial and extremely complex. Genetic variability and genome plasticity cause not only the available drugs to have limitations, but also make the search for new drugs challenging. Here, we examined the biological characteristics of parasites that hinder drug discovery.