Resumen: The range of application of methodologies of complexity science, interdisciplinary by nature, has spread even more broadly across disciplines after the dawn of this century. Specifically, applications to public policy and corporate strategies have proliferated in tandem. This paper reviews the most used complex systems methodologies with an emphasis on public policy. We briefly present examples, pros, and cons of agent-based modeling, network models, dynamical systems, data mining, and evolutionary game theory. Further, we illustrate some specific experiences of large applied projects in macroeconomics, urban systems, and infrastructure planning. We argue that agent-based modeling has established itself as a strong tool within scientific realm. However, adoption by policy-makers is still scarce. Considering the huge amount of exemplary, successful applications of complexity science across the most varied disciplines, we believe policy is ready to become an actual field of detailed and useful applications.