Dating back to the 60's the petrochemical process industry has been a pioneer in the application of mathematical programming, mostly in the form of linear programming, for production planning, despite the nonlinearities that are encountered in process models. In contrast, in process scheduling the industry has historically relied on heuristics and ad-hoc spreadsheet tools. However, in the last 10-15 years, given important advances in mixed-integer linear and nonlinear programming, there has been a strong move towards the use of mathematical programming in the area of scheduling. Furthermore, these advances have also promoted the holistic and more ambitious view of optimizing entire supply chains, consisting of suppliers, manufacturing plants and distribution centers, which has led to the goal of performing enterprise-wide optimization. In this presentation we discuss some of these developments, and emphasize future challenges that need to be overcome to realize the vision of Enterprise-wide Optimization. We specifically discuss challenges related to modeling, multi-scale optimization, optimization under uncertainty and algorithmic and computational developments that need to be overcome to make enterprise-wide optimization a reality. It is our belief that a multidisciplinary approach from chemical engineering and operations research is required to make significant progress in this area through the combination of advances in modeling of scheduling, planning and supply chains, and mathematical programming techniques for mixed-integer, disjunctive, global optimization and stochastic programming. We provide several examples of recent successful industrial applications in planning and scheduling of petroleum and chemical facilities that are clearly pointing to achieving the goal of Enterprise-wide Optimization.