Probabilistic and percentile/quantile functions play an important role in several applications, such as finance (Value-at-Risk), nuclear safety, and the environment. Recently, significant advances have been made in sensitivity analysis and optimization of probabilistic functions, which is the basis for construction of new efficient approaches. This work presents the state-of-the-art in the theory of optimization of probabilistic functions and several engineering and finance applications, including material flow systems, production planning, Value-at-Risk, asset and liability management, and optimal trading strategies for financial derivatives (options).