Deterministic optimization approaches have been well developed and widely used in the process industry to accomplish off-line and on-line process optimization. The challenging task for the academic research currently is to address large-scale, complex optimization problems under various uncertainties. Therefore, investigations on the development of stochastic optimization approaches are needed. In the last few years we proposed and utilized a new solution concept to deal with optimization problems under uncertain operating conditions as well as uncertain model parameters. Stochastic optimization problems are solved with the methodology of chance constrained programming. The problem is to be relaxed into an equivalent nonlinear optimization problem such that it can be solved by a nonlinear programming (NLP) solver. The major challenge towards solving chance constrained optimization problems lies in the computation of the probability and its derivatives of satisfying inequality constraints. Approaches to addressing linear, nonlinear, steady-state as well as dynamic optimization problems under uncertainty have been developed and applied to various optimization tasks with uncertainties such as optimal design and operation, optimal production planning as well as optimal control of industrial processes under uncertainty. In this paper, a comprehensive summary of our recent work on the theoretical development and practical applications is presented. (C) 2007 Published by Elsevier Ltd.