Process plants have to operate in an increasingly dynamic environment, due to factors such as increased market volatility, variation in product demand, and electricity price fluctuations. Dynamic optimization provides a means to determine economically optimal operating policies, as well as designs that have attractive dynamic characteristics. Key challenges are that high fidelity models of industrial process systems are typically nonlinear and of high dimension. Consideration of uncertainty within the optimization formulation increases the problem dimension even further. This presentation will provide an overview of dynamic optimization methods suitable for large-scale industrial problems. Formulations for both optimal operation and design will be described, and illustrated through industrial case studies. Challenges will be discussed, and promising future research directions identified.