This study explored the potential of digital games as learning environments to develop mindsets capable of dealing with complexity in the domain of sustainability. Building sustainable futures requires the ability to deal with the complex dynamics that characterize the world in which we live. As central elements in this system, we must develop the ability of constantly assessing the environment that surrounds us, operating in it and adapting to it through a continuous and iterative individual and interpersonal process of revision of our frames of reference. We must focus on our world as a whole, considering both immediate problems and long-term consequences that decision making processes could generate. Educating for sustainability demands learning approaches and environments that require the development of systems thinking and problem-solving, rather than solely the acquisition of factual knowledge. When designed with complexity in mind, digital games present a high potential to facilitate sustainability learning. Digital games can be modelled as complexified systems, engaging players in cognitively demanding tasks requiring problem-solving and decision-making skills to deal with ill-structured problems, unpredictable circumstances, emerging system properties and behaviours, and non-linear development of events. Furthermore, games can require players to collectively engage in the pursuit of common goals, promoting remote interactions across large numbers of players. To understand how games are currently used for "learning for sustainability", we analysed 20 games. In spite of the potential offered by digital games and concrete examples of good practice, we found that sustainability thematic contextualisation and complex system dynamics are not leveraged as much as could be expected. Hence, there seems to be space for improvements oriented at creating game systems requiring players to address sustainability issues from multiple perspectives through: contextualisation integrating the social, economic and environmental dimensions of sustainability; gameplay dynamics integrating non-linearity, emergence, uncertainty, ill-defined problems and social interactions. (Contains 5 figures.)