Chagas disease (CD) still imposes a heavy burden on most Latin American countries. Vector-borne and mother-to-child transmission cause several thousand new infections per year, and at least 5 million people carry Trypanosoma cruzi. Access to diagnosis and medical care, however, is far from universal. Starting in the 1990s, CD-endemic countries and the Pan American Health Organization-World Health Organization (PAHO-WHO) launched a series of multinational initiatives for CD control-surveillance. An overview of the initiatives' aims, achievements, and challenges reveals some key common themes that we discuss here in the context of the WHO 2030 goals for CD. Transmission of T. cruzi via blood transfusion and organ transplantation is effectively under control. T. cruzi, however, is a zoonotic pathogen with 100+ vector species widely spread across the Americas; interrupting vector-borne transmission seems therefore unfeasible. Stronger surveillance systems are, and will continue to be, needed to monitor and control CD. Prevention of vertical transmission demands boosting current efforts to screen pregnant and childbearing-aged women. Finally, integral patient care is a critical unmet need in most countries. The decades-long experience of the initiatives, in sum, hints at the practical impossibility of interrupting vector-borne T. cruzi transmission in the Americas. The concept of disease control seems to provide a more realistic description of what can in effect be achieved by 2030.