We discuss models and data of crowd disasters, crime, terrorism, war and disease spreading to show that conventional recipes, such as deterrence strategies, are not effective and sufficient to contain them. The failure of many conventional approaches results from their neglection of feedback loops, instabilities and/or cascade effects, due to which equilibrium models do often not provide a good picture of the actual system behavior. However, the complex and often counter-intuitive behavior of social systems and their macro-level collective dynamics can be understood by means of complexity science, which enables one to address the aforementioned problems more successfully. We highlight that a suitable system design and management can help to stop undesirable cascade effects and to enable favorable kinds of self-organization in the system. In such a way, complexity science can help to save human lives.