Human African trypanosomiasis is a neglected tropical disease caused by the extracellular protozoan parasite Trypanosoma brucei, and targeted for eradication by 2030. The COVID-19 pandemic contributed to the lengthening of the proposed time frame for eliminating human African trypanosomiasis as control programs were interrupted. Armed with extensive antigenic variation and the depletion of the B cell population during an infectious cycle, attempts to develop a vaccine have remained unachievable. With the absence of a vaccine, control of the disease has relied heavily on intensive screening measures and the use of drugs. The chemotherapeutics previously available for disease management were plagued by issues such as toxicity, resistance, and difficulty in administration. The approval of the latest and first oral drug, fexinidazole, is a major chemotherapeutic achievement for the treatment of human African trypanosomiasis in the past few decades. Timely and accurate diagnosis is essential for effective treatment, while poor compliance and resistance remain outstanding challenges. Drug discovery is on-going, and herein we review the recent advances in anti-trypanosomal drug discovery, including novel potential drug targets. The numerous challenges associated with disease eradication will also be addressed.