The author's vision of the meanings, perceptions and assessments of risks in the conditions of the “new normal” - fault lines, confrontation and crises of the era of bifurcation is presented. The analysis is based both on a study of the best anti-crisis risk management practices, and on my own experience as one of the founders and organizers of the development of a risk management system in the energy and nuclear power engineering industries. It is shown that natural science approaches (system analysis, mathematical modeling methods, tools of nonequilibrium gas thermodynamics, new theories of chaos) can be effective in identifying, analyzing and forecasting socio-economic and political processes, especially during periods of crises, disequilibrium, instability and turbulence of complex systems. Methods are proposed for transforming the mentality of society in order to move to a qualitatively new level of understanding, analysis and risk management of unpredictable and difficult to formalize changes in the era of bifurcations.