This study traces the origin, evolution, and current state-of-the-art of engineering-oriented water-quality management and modeling. Three attributes of polluted water underlie human concerns for water quality: rubbish (aesthetic impairment), stink (ecosystem impairment), and death (public health impairment). The historical roots of both modern environmental engineering and water-quality modeling are traced to the late nineteenth and early twentieth centuries when European and American engineers worked to control and manage urban wastewater. The subsequent evolution of water-quality modeling can be divided into four stages related to dissolved oxygen (1925-1960), computerization (1960-1970), eutrophication (1970-1977) and toxic substances (1977-1990). Current efforts to integrate these stages into unified holistic frameworks are described. The role of water-quality management and modeling for developing economies is outlined.