Risk is a central theme in financial market theory. Because risk is an abstract concept, its measurement is not a priori clear as with return. This chapter focuses on the most important risk measures in today’s financial industry, namely value-at-risk and expected shortfall. To comprehend their origins involves understanding the origin of modern finance. Under the mean-variance paradigm of Markowitz’s portfolio theory, risk is defined as the variance of an investment. However, this symmetric measure can be an inappropriate concept to serve as a risk measure. The chapter provides a discussion of the different suggestions presented in the academic literature including the concepts of modern risk measures. These risk measures also have deficiencies, not only when managers use them to control for specific portfolios but also when regulators use them as a tool to safeguard financial markets against systemic risks.