Leishmaniases are a group of vector-borne diseases caused by infection with the protozoan parasites Leishmania spp. Some of them, such as Mediterranean visceral leishmaniasis, are zoonotic diseases transmitted from vertebrate to vertebrate by a hematophagous insect, the sand fly. As there is an endemic in more than 90 countries worldwide, this complex and major health problem has different clinical forms depending on the parasite species involved, with the visceral form being the most worrying since it is fatal when left untreated. Nevertheless, currently available antileishmanial therapies are significantly limited (low efficacy, toxicity, adverse side effects, drug-resistance, length of treatment, and cost), so there is an urgent need to discover new compounds with antileishmanial activity, which are ideally inexpensive and orally administrable with few side effects and a novel mechanism of action. Therefore, various powerful approaches were recently applied in many interesting antileishmanial drug development programs. The objective of this review is to focus on the very first step in developing a potential drug and to identify the exploratory methods currently used to screen in vitro hit compounds and the challenges involved, particularly in terms of harmonizing the results of work carried out by different research teams. This review also aims to identify innovative screening tools and methods for more extensive use in the drug development process.