Many limitations of contemporary process management systems (PrMS) can be traced back to the missing integration of processes and data. A unified understanding of the inherent relationships existing between processes and data, however, is still missing. In the PHILharmonicFlows project we figured out that process support often requires object-awareness. This means, data must be manageable in terms of object types comprising object attributes and relations to other object types. In this paper, we systematically introduce the fundamental characteristics of object-aware processes. Further, we elaborate existing approaches recognizing the need for a tighter integration of processes and data along these characteristics. This way, we show the high relevance of the identified characteristics and confirm that their support is needed in many application domains.