Industry 4.0 is a concept that has attracted much research and development over the last decade. At its core is the need to connect physical devices with their digital representations which essentially means establishing a digital twin. Currently, the technological development of digital twins has gathered much attention while the organizational and business aspects are less investigated. In response, the suitability of enterprise modeling and capability management for the purpose of developing and management of business-driven digital twins has been analyzed. A number of requirements from literature are summarized and two industrial cases have been analyzed for the purpose of investigating how the digital twin initiatives emerge and what forces drive the start of their implementation projects. The findings are discussed with respect to how Enterprise Modeling and the Capability-Driven Development method are able to support the business motivation, design and runtime management of digital twins.