In civil engineering, carbon is typically regarded as a modern material to serve as reinforcement in concrete structures. Compared to steel reinforcement, it features two substantial benefits: It is not sensitive to corrosion, and has an enormously increased tensile strength. In contrast, carbon reinforcement is sensitive to lateral pressure and lacks the property of strain hardening. As a first step of establishing carbon reinforced concrete as a new building composite material, carbon reinforcement has basically served to replace the state-of-the-art steel reinforcement. This target led topioneering findings with respect to determining the material properties of the composite and developing advanced individual components. However, barely substituting steel by carbon does not allow to fully utilize the carbon's benefits while its disadvantageous properties reveal the limits of this approach. Instead, novel design principles are required to meet the material's nature aiming at appropriately using its beneficial properties. Currently, new construction principles are being researched for high performance building material combinations such as textile and carbon reinforced concrete. This paper provides an overview of baselines in the preliminary stages of this research. The overview includes history, inspiration, concrete matrices, non-metallic reinforcement, structural elements, modeling, production, tomography, and sustainability. The objective of the study is to provide a baseline for the envisaged development of principles for future construction: radically new concepts for the design, modeling, construction, manufacturing, and use of sustainable, resourceefficient building elements made of mineral building materials with the aim of entirely benefiting from the materials' potential.