Fiber reinforced polymer (FRP) reinforcements combine high strength with low weight and have a high corrosion resistance. Due to these beneficial characteristics, the use of FRP reinforcement in concrete structures has been established and investigated over the last 30 years as a suitable solution for sustainable and long-lasting concrete constructions. In particular, carbon fiber reinforced polymer (CFRP) tendons have a high potential to be applied as prestressing reinforcement due to their higher stiffness and tensile strength as well as better durability compared to reinforcements using glass or aramid fibers. CFRP tendons have been successfully used in many bridge projects in the United States and Canada. Nevertheless, the application of CFRP prestressing tendons in bridge design is not common. The main reasons for the limited implementation of this technology are the lack of standardized material properties as well as consistent and approved design guidelines. To enable a widespread and feasible application of CFRP tendons, comprehensive design methods, comparable to those for steel prestressed concrete structures, are necessary. Furthermore, the design guidelines have to comply with reliability requirements to guarantee the safety of the structures. In the present thesis, the behavior of prestressed concrete beams with CFRP tendons at the ultimate limit state is analyzed in detail. Based on the results, suitable design methods are developed. The transfer of the prestressing force and the tendon anchorage are important design aspects for the construction of pre-tensioned concrete structures. Based on experimental investigations and results from literature, detailing provisions are defined to avoid splitting cracks in the transfer zone and to secure an undisturbed transfer of the prestressing force. Moreover, a theoretical model is derived to determine both the transfer and development length of CFRP tendons depending on their bond characteristics. Using probabilistic calibration, a design model meeting the reliability requirements of Eurocode 0 is proposed. Besides the bond behavior, the flexural strength is a main aspect of the design of beams prestressed with CFRP tendons. Based on the concept of a balanced reinforcement ratio, a flexural resistance model is derived in compliance with Eurocode 2. To develop an appropriate design model, a reliability analysis is performed using stochastic simulations to determine the governing safety factor for the CFRP tendons. For this purpose, two footbridge concepts with prestressed CFRP reinforcement are investigated. To avoid brittle shear failures, the shear strength of reinforced concrete beams has to be verified at ultimate limit state. To extend the database of shear tests on prestressed beams with FRP reinforcement, beams with textile shear reinforcement and prestressed CFRP tendons are tested. Furthermore, theoretical investigations are conducted to derive a shear design model for prestressed and non-prestressed beams with FRP shear reinforcement. For this purpose, a truss model with variable strut inclination is developed. The angle of the compression strut is derived based on a compression field model originally developed for steel reinforced beams.