The need for semantics preserving integration of complex data has been widely recognized in the healthcare domain. While standards such as Health Level Seven (HL7) have been developed in this direction, they have mostly been applied in limited, controlled environments, still being used incoherently across countries, organizations, or hospitals. In a more mobile and global society, data and knowledge are going to be commonly exchanged between various systems at Web scale. Specialists in this domain have increasingly argued in favor of using Semantic Web technologies for modeling healthcare data in a well formalized way. This paper provides a reality check in how far current Semantic Web standards can tackle interoperability issues arising in such systems driven by the modeling of concrete use cases on exchanging clinical data and practices. Recognizing the insufficiency of standard OWL to model our scenario, we survey theoretical approaches to extend OWL by modularity and context toward...