The recent financial crisis highlighted the need for risk measures that deal adequately with extreme events. In the modern complex financial world, risk measures can only be effective if they take into consideration the endogeneity of risk. Endogenous risk is an inherent characteristic of the modern financial system. The crisis has also highlighted the considerable changes in investors' attitude towards risk under changing market conditions. These developments have cast doubt on the role of traditional elements of risk management theory: prices, probabilities and preferences. The paper presents a non-technical summary of the main challenges for effective risk management in the modern complex financial world.