We then present a spatio-temporal optimization model that illustrates various biological and economic aspects of an ISM problem. We first define key concepts in invasive species management (ISM) in a framework that characterizes biological invasions, associated economic and environmental costs, and their management. In this paper, we summarize the mathematical models applied to optimize invasive species prevention, surveillance, and control. Operations research methods, such as mathematical programming models, are powerful tools for evaluating different management strategies and providing optimal decisions for allocating limited resources to control invaders. The effective management of invasive species is a highly complex problem requiring the development of decision tools that help managers prioritize actions most efficiently by considering corresponding bio-economic costs, impacts on ecosystems, and benefits of control. The international community, including the United Nations' Global Invasive Species Program (GISP), National Invasive Species Council (NISC), and Center for Invasive Species Management (CISM), has called for a rapid control of invaders in order to minimize their adverse impacts. Invasive species are a major threat to the economy, the environment, health, and thus human well-being.