In traditional portfolio theory, risk management is limited to the choice of the relative weights of the riskless asset and a diversified basket of risky securities, respectively. Yet in industry, risk management represents a central aspect of asset management, with distinct responsibilities and organizational structures. We identify frictions that lead to increased importance of risk management and describe three major challenges to be met by the risk manager. First, we derive a framework to determine a portfolio position's marginal risk contribution and to decide on optimal portfolio weights of active managers. Second, we survey methods to control downside risk and unwanted risks since investors frequently have non-standard preferences which make them seek protection against excessive losses. Third, we point out that quantitative portfolio management usually requires the selection and parametrization of stylized models of financial markets. We therefore discuss risk management approaches to deal with parameter uncertainty, such as shrinkage procedures or resampling procedures, and techniques of dealing with model uncertainty via methods of Bayesian model averaging.