People often learn about various crises leading to catastrophes in nature, in social and economic life, or in living organisms (including humans). The book offers a popular account of the causative mechanisms of critical and catastrophic states in a broad range of natural and cultural systems -- which obey the same laws -- and thus makes the reader aware of the reasons and ways to avoid and mitigate the negative consequences of catastrophic events. The authors apply a single mathematical approach to investigate the revolt of cancer cells that destroy organisms and population outbreaks that destroy the natural ecosystems. The approach is also applied to the interference of industry with the environment that often leads to ecology and economic collapses, global catastrophes, and economic and social crises.