A symbiotic simulation system (S3), sometimes also called a 'digital twin', enables interactions between a physical system and its computational model representation. With the goal of supporting operational decisions, an S3 uses real-time data from the physical system, which is gathered via sensors. This real-time data is also saved in an enterprise data storage system (EDSS), so it can be used as historical data for future use. Both real-time and historical data are then used as inputs to the different components of an S3, which typically comprises several modules: data acquisition, simulation, optimisation, machine learning, and an 'actuator'. The latter is needed when there is not a human agent between the S3 and the system. Given the amount of data generated by today's smart systems, an S3 needs to be coupled with an EDSS. Furthermore, the S3 may produce a large amount of output data that needs to be stored, since it might be re-used by the machine learning module to make the S3 adaptive in dynamic scenarios. With the goal of supporting real-time operational decision-making -specially in Industry 4.0 applications such as smart cities, smart factories, intelligent transportation systems, and digital supply chains -, this paper proposes a generic system architecture for an S3 and discusses its integration within EDSSs. Moreover, the paper reviews the state-of-the-art in S3, and analyses how these systems can interact with EDSSs to make real-time decision making a reality. Finally, the paper also points out several research challenges in S3.