Business Process Modeling is increasingly important for the digitalization of both IT and non-IT business processes, as well as for their deployment on service-oriented architectures. A number of methodologies, languages, and software tools have been proposed to support digital business process design; nonetheless, a lot remains to be done for assessing a business process model validity with respect to an existing organizational structure or external constraints like the ones imposed by security compliance regulations. In particular, web-based business coalitions and other inter-organizational transactions pose a number of research problems. The Model Driven Architecture (MDA) provides a framework for representing processes at different levels of abstraction. In this paper, a MDA-driven notion of business process model is introduced, composed of a static domain model including the domain entities and actors, plus a platform-independent workflow model providing a specification of process activities. The paper focuses on semantics-aware representation techniques, introducing logics-based static domain models and their relationship with Description Logics and current Semantic Web metadata formats. Then, the paper discusses some issues emerging from the literature on business processes representation and presents some research directions on the evaluation of the compatibility of business and IT processes with existing organizational environments and practices. The problem of implicit knowledge and of its capture in a manner which allows it to be included in business process design is also discussed, presenting some open research issues.