This paper presents first a brief overview of the considerable work that has been performed for the systematic synthesis of process flowsheets and corresponding subsystems. Next, it is argued that a number of important research challenges remain to be solved with major themes being fundamental integration of different synthesis methodologies, improved robustness of optimization-based methods for predicting solutions of good quality, and improved capabilities for handling larger problems. In order to illustrate how some of these challenges are being addressed with the use of optimization-based techniques, we describe work in the areas of integration of logic in mixed-integer optimization, global optimization of nonlinear programming models, and rigorous preliminary screening for MINLP models. Numerical results will be presented to illustrate the usefulness and potential of these methods.