Terrestrial and marine biodiversity provides the basis for both ecosystems functioning and numerous commodities or services that underpin human well-being. From several decades, alarming trends have been reported worldwide for both biodiversity and ecosystem services. Therefore the sustainable management of biodiversity requires a double viewpoint balancing ecological conservation with the welfare of human societies. Understanding the underlying trade-offs, synergies and interactions imposes the development of interdisciplinary researches and methods. In that respect, bio-economic or ecological economic modeling is likely to play a major role. The present paper intends to elicit the key features, strengths and challenges of bio-economic approaches especially in mathematical and computational terms. It first recall the main bio-economic methods, models and decisional instruments used in these types of analyses. Then the paper shows to what extent bio-economic sustainability lies between equilibrium, viability and optimality mathematical frameworks. It ends up by identifying new major challenges among which the operationalization of ecosystem based management, the precautionary principle and the implementation of governance are especially important. Computational Management Science Computational Management Science Look Inside