Research in computational sustainability seeks to develop and apply methods from computer science to the many challenges of managing the earth's ecosystems sustainably. Viewed as a control problem, ecosystem management is challenging for two reasons. First, we lack good models of the function and structure of the earth's ecosystems. Second, it is difficult to compute optimal management policies because ecosystems exhibit complex spatio-temporal interactions at multiple scales. This talk will discuss some of the many challenges and opportunities for machine learning research in computational sustainability. These include sensor placement, data interpretation, model fitting, computing robust optimal policies, and finally executing those policies successfully. Examples will be discussed on current work and open problems in each of these problems. All of these sustainability problems involve spatial modeling and optimization, and all of them can be usefully conceived in terms of facilitating or preventing flows along edges in spatial networks. For example, encouraging the recovery of endangered species involves creating a network of suitable habitat and encouraging spread along the edges of the network. Conversely, preventing the spread of diseases, invasive species, and pollutants involves preventing flow along edges of networks. Addressing these problems will require advances in several areas of machine learning and optimization.