As a result of a universal drive for more consistent attainment of high product quality, more efficient use of energy, and tighter safety and environmental regulations, industrial processes have evolved over the past few decades into very complex and highly integrated systems. Such stringent demands naturally create more difficult and challenging control problems for today's industrial process control engineer -problems requiring more sophisticated solutions than can be provided by traditional techniques alone. This paper provides an overview of some of the jmportant contemporary challenges of industrial process control, noting the fortunate circumstance of the emergence of pow:rful digital computer technology just in time to facilitate the analysis, design and implementation or the sophisticated control techniques required to take on these challenging problems. A specific case study involving the control of a commercial polymerization reactor is used to illustrate concretely the scope of the problems and challenges, and the role of the digital computer in how such problems are being handled.