Safety-critical dynamic systems are ubiquitous and essential to quality of life. For example, breast cancer cell populations must be managed using tolerable therapeutic regimens despite uncertainties in drug-drug interactions. Further, stormwater catchments must avoid large overflows despite capacity constraints and unknown future rainfall. In the robust control paradigm, a controller is synthesized by assuming that worst-case outcomes with respect to a dynamic system model are indicative of real-world outcomes. I will first present dynamic system models of drug-treated breast cancer cell populations that I have developed in collaboration with cancer biologists at the Oregon Health and Science University. In addition to providing biological insights, these models have motivated the theoretical development of robust drug schedules that (under certain conditions) are guaranteed to induce exponential decay in cancer cell populations. Second, I will present joint work with the Berkeley Water Center, in which we show that Hamilton-Jacobi reachability analysis can provide improved design-phase indicators of stormwater catchment operation. Although robust control methods (such as those above) have safety guarantees in theory, the utility of these methods in practice is substantially limited by the hard-to-quantify uncertainties of real-world systems. In the last part of my talk, I will discuss current work towards deriving more realistic safety guarantees via the emerging paradigm of risk-sensitive control. Specifically, I will present a risk-sensitive reachability theory for safety of stochastic systems based on the Conditional Value-at-Risk measure and a numerical example inspired from stormwater catchment design.