Recent research has highlighted environmental sustainability as a key issue of concern affecting the future of human wellbeing. To pursue a sustainable future of a system, it is a critical challenge to make decisions at all levels of management. Decision making for controlling or steering a system requires models of the system that represent the determining characteristics of the system and have sufficient predictive power. Practitioners/researchers of environmental management use a large variety of (types of) models to support decision making, and it has become a complex task to select the appropriate model-type for a desired management goal. This paper considers the most common types of models and uses the mathematical properties of these model types to discuss the pros and cons of their use in environmental management / decision making. We explore how these mathematical properties influence the feasibility, viability and validity of the use of such models.