Current process management systems (PMS) use graphical modelling languages such as BPMN for modelling the control flow. Almost no program code has to be written by business process designers for defining the possible order of activities. For another important aspect of business processes – assigning actors to activities – no such simple and standardized way of modelling exists. This causes problems at business process implementation projects in practice. We explain such aspects and shortcomings of current commercial PMS that lead to these problems. For each aspect, it is analysed whether appropriate scientific solutions exist, or whether it is an unsolved research question.