This project focuses on the realization and application of trapped Rydberg ions for quantum information processing and quantum simulation. It will bring together two prospective quantum computational systems: trapped ions and Rydberg atoms. Joining them will form a novel quantum system with advantages from both sides.This approach will open a new path of investigation for quantum computing and simulation and will allow investigation of different physical qualities not yet addressed in the existing systems. In particular, it promises to speed up entangling interactions by three orders of magnitude and to extend the interaction distance by at least a factor of two between neighbouring ions. The higher speed of entangling interactions would allow the execution of more complex quantum algorithms before decoherence destroys the stored quantum information. The increased coupling distance would enable the controlled interaction of neighbouring ions which are trapped individually. This would allow setting up a quantum computational system formed by a Coulomb crystal or a two-dimensional array of individually trapped ions.Such qualities make trapped Rydberg ions a powerful alternative approach for scalable quantum information processing. In particular, a string, crystal or two-dimensional array of interacting trapped Rydberg ions can be used for simulations of complex quantum systems intractable by classical computers.