Uncertain systems that evolve over time (called stochastic dynamical systems) are all around us. Examples include a patient that is fighting cancer and the combined sewer system in the city of Toronto. Typically, we design systems to operate under uncertainty by invoking one of two perspectives. Either we assume the worst possible circumstances, or we assume average circumstances. More broadly, we may wonder whether it is possible to equip systems with a flexible awareness of the vast spectrum of possibilities between the average case and the worst case. Towards this long-term goal, I will introduce the area of risk-aware control theory and highlight our methodology of risk-aware safety analysis. I will present the core mathematical machinery, which uses conditional value-at-risk (a risk measure from finance) and dynamic programming on an augmented state space (to record incurred costs). I will also discuss current directions to alleviate the curse of dimensionality.