The simplest approach to describe the evolution of a system is the linear one. A system can indeed behave as linear also when many variables are driving its dynamics and, in this case, a mathematical description, even if very complicated, can allow accurate predictions for the future conditions of the system itself. On the contrary, the behavior of complex systems is intrinsically difficult to model due to the dependencies, relationships, or other types of interactions between their parts or the environment. Systems that are "complex" have peculiar properties that arise from these relationships, such as nonlinearity, emergence, self-organization, adaptation, and feedback loops, etc., and they cannot be understood by the independent knowledge of their parts. The socio-economic systems, where a diversity of variables and stakeholders are deeply and often indirectly cross-linked, can show abrupt changes and trigger unexpected or undesired scenarios. Addressing complexity requires therefore multi and cross-disciplinarity, but this could not be enough, especially when decisions are requested to impact in long-term and global scenarios, where the interactions between the human activities and the environment are transforming the trans-national relations too. The understanding of the concept of complexity, the identification of essential variables and scales (in time and space), the simplification, optimization and applicability of modeling, the computational implications of complexity, are crucial when the option assessments are involved in decision-making and communication processes.