If you accept the argument that risk matters and that it affects how managers and investors make decisions, it follows logically that measuring risk is a critical first step towards managing it. In this chapter, we look at how risk measures have evolved over time, from a fatalistic acceptance of bad outcomes to probabilistic measures that allow us to begin getting a handle on risk, and the logical extension of these measures into insurance. We then consider how the advent and growth of markets for financial assets has influenced the development of risk measures. Finally, we build on modern portfolio theory to derive unique measures of risk and explain why they might be not in accordance with probabilistic risk measures.