This talk discusses various types of uncertainties existing in engineering systems including random and fuzzy uncertainties.Different theories for modeling these uncertainties are briefly discussed.The focus of the talk is then put on the solution methods for nonlinear dynamical systems with uncertainties, in particular, the cell mapping methods, originally developed by C.S.Hsu of UC Berkeley.Concepts of generalized cell mappings and normal forms of the transition probability matrix are discussed.The generalized cell mappings can be conceptually viewed as a database of short-time solutions in the region of interest in the state space.The generalized cell mapping method is thus compared favorably with the time-domain long-term numerical simulation approach.We further point out that the generalized cell mapping is amenable to massive parallel computing.Examples are presented including benchmark mathematical optimization problems, and optimal designs of feedback controls and fractional damping.