In real life, many combinatorial and economic problems have nonlinear objectives and constraints, where the nonlinearities typically arise from different risk preferences, non-rationality, etc. Solving these problems is often computationally hard but can be beneficial by providing more revenue or welfare. In this thesis, I am going to investigate three problems: route planning with a nonlinear objective, dynamic mechanism design with agents of bounded rationality, and economic mechanism design with risk-loving buyers.