Abstract: Most of the research efforts so far have been in developing efficient algorithms for different applications, assuming ideal inputs with precisely defined computational domains. Recently, there has been a growing interest in verification and validation of numerical simulations and in modeling uncertainty. The more general question thus becomes how to model uncertainty and stochastic inputs, and formulate algorithms to accurately reflect the propagation of uncertainty. Different approaches for stochastic modeling and uncertainty quantification will be discussed, with the focus on their applications to complex engineering problems. These approaches include the classical methods such as perturbation expansion and more recently developed methods such as Generalized Polynomial Chaos (gPC). gPC is essentially a spectral approximation of functionals in random space. It represents random processes spectrally via orthogonal polynomial functionals and can achieve fast convergence. Combined with either a stochastic Galerkin or stochastic collocation approach, the governing equations (stochastic ODEs/PDEs) are reduced to a set of deterministic differential equations which can be solved by conventional numerical techniques. In addition to the mathematical framework, I will also discuss computational challenges/opportunities associated with stochastic modeling, especially for complex engineering systems, and present various applications.