Roger W.H. Sargent (1926–2018) was an unprecedented pioneer who foresaw the role that mathematical and computational tools would have in chemical engineering. His visionary work created the multidisciplinary field of Process Systems Engineering (PSE), a field that acts as a central hub influencing all subfields of chemical engineering. His particular interest in optimal control applied to industrial processes led him to develop numerical techniques to solve large-scale optimal control problems. In this work, a brief overview of the theory of optimal control is offered, spanning from its roots in calculus of variations to Pontryagin's maximum principle and some of its extensions. Furthermore, important contributions made by Sargent and his students are presented. Selected applications currently found in literature are presented as well–ranging from classical chemical engineering systems to bioprocesses. Some future perspectives of the field are also presented in the concluding section.