  Uncertainty is prevalent in engineering design, data-driven problems, and
decision making broadly. Due to inherent risk-averseness and ambiguity about
assumptions, it is common to address uncertainty by formulating and solving
conservative optimization models expressed using measures of risk and related
concepts. We survey the rapid development of risk measures over the last
quarter century. From their beginning in financial engineering, we recount the
spread to nearly all areas of engineering and applied mathematics. Solidly
rooted in convex analysis, risk measures furnish a general framework for
handling uncertainty with significant computational and theoretical advantages.
We describe the key facts, list several concrete algorithms, and provide an
extensive list of references for further reading. The survey recalls
connections with utility theory and distributionally robust optimization,
points to emerging applications areas such as fair machine learning, and
defines measures of reliability.
