The objective of this work is to develop both theory and formal optimization-based numerical techniques for the optimal design of process and control systems under uncertainty. While previous work mainly concentrated on steady-state considerations and time-invariant uncertainty, the emphasis in this thesis is on the use of dynamic mathematical models to describe the process system and time-varying uncertainty. Flexibility considerations, robust stability criteria and explicit control structure selection and controller design aspects are considered as an integral part of the process synthesis/design task. For the incorporation of flexibility and control system design in process design and optimization, a mixed-integer stochastic optimal control formulation was proposed, the solution of which results in process design and control systems which are economically optimal while being able to cope with parametric uncertainty and process disturbances. Regarding robust stability criteria, a combined flexibility-stability analysis method was developed which provides a quantitative measure of the size of the parameter space over which feasible and stable operation can be attained by proper adjustment of the control variables. Such an analysis step can then be included in the simultaneous process and control design formulation. Algorithms and numerical techniques for the solution of the resulting mathematical formulations have also been developed. In particular, an iterative decomposition algorithm was proposed, which alternates between two subproblems: A multiperiod design subproblem, which determines the process and control structure and design to satisfy a set of critical uncertain parameters over time, and the combined flexibility-stability analysis step, which identifies a new set of critical parameters for a fixed design and control. Since both steps of the algorithm involve the solution of mixed-integer optimal control formulations, a novel technique for the solution of this class of problems was also proposed, featuring an implicit Runge-Kutta method for time discretization, an efficient integration step size selection procedure and adjoint equations for obtaining the reduced gradients. Numerical examples together with detailed process design examples, such as a ternary distillation system and a binary double effect distillation system, are also presented to demonstrate the potential of the proposed methodology.