In the Project C³ – Carbon Concrete Composite, an interdisciplinary consortium of more than 160 partners is currently underway researching carbon reinforced concrete construction. The “CUBE” building, represented in Figure 1, exemplifies the results of this project, and it is assumed to be the world’s first building, constructed entirely of non-metallic, carbon reinforced concrete, which will be completed in 2021. The main purpose of the building that has got a gross floor area of about 220 m² is to show that the C³ construction method has progressed so far that the entire process chain can be passed through, including the design, planning, tendering, construction and operation. Additionally, the building provides a testing facility site where innovative components of multiple future research projects can be implemented and tested under realistic conditions. This paper presents this very challenging and trend-setting building project. In detail, it deals with the architecture, the bearing structure, individual components and their special features. In particular, the high-performance building material carbon reinforced concrete and its usage in buildings, both for prefabricated and in-situ manufactured components, are presented. Additionally, the resulting advantages over classical building materials are shown and discussed. Finally, the article shows the large and diverse application potential of carbon reinforced concrete and its future fields of application.