Systemic risks, as opposed to conventional risks, bear the danger of destroying entire systems. Their understanding and governance remain a serious challenge. The phenomena of systemic risks show many analogies with those of dynamic structure generation in the systems of nature, technology, and society, including simple model systems of physics and chemistry. By analyzing these model systems, the elementary processes and the generic mechanisms by which they generate macroscopic dynamic structures become evident. Generalizing these insights makes it possible to formulate the basic framework of a theory of systemic risks with elements providing hints for adequate governance strategies. Although these insights cannot be applied to societal processes one by one, they reveal generic patterns and clusters.