Some of the key issues associated with the equation-oriented approach to process modelling and simulation are examined. It is argued that most processes and operations of industrial interest have combined discrete and continuous characteristics. Furthermore, effective tools for describing both the physical behaviour of process systems, and the external control actions and disturbances imposed on them are required. In both areas, major concerns include managing the complexity of real processes, and supporting the development of general components that can be re-used within a number of different applications. Recent work in this direction is reviewed. A general mathematical statement for the combined discrete and continuous dynamic simulation problem is presented, and the use of symbolic, structural and numerical solution techniques is discussed. Methods for the diagnosis of problems that are either badly-posed or difficult to solve with currently available methods are also considered. The areas of modelling distributed parameter systems, and supporting the formal description and solution of general optimisation problems are identified as being of strategic importance for the future evolution of general-purpose process modelling environments.