Trapped ion systems are one of the leading technologies for the development of various novel quantum devices, including computers, simulators and enhanced sensors. Ion traps offer a high level of control in terms of both the electronic and motional states of individual quantum systems. This enables information to be efficiently encoded and transferred, often via interaction with highly controlled laser fields. In particular, the use of collective motional excitation to generate entanglement is a principle that underlies the majority of gate operations that have thus far been implemented in trapped ion systems. Another method, originally devised to circumvent the need for collective motional excitation in entangling operations, is to use Rydberg states which can be engineered to produce strong, direct and state-dependent interactions between ions. Due to their sensitivity to electric fields, trapped Rydberg ions have also opened the possibility for the development of entirely new gate schemes and for use in quantum metrology. In this work we employ the high level of motional control available to trapped ion systems in order to perform three experiments, involving quantum simulation, computation and metrology respectively. In the first we make use of a single ion and couple its electronic and motional states to simulate sub- and superradiant emission for an atom confined in a 2D cavity. The results obtained showed that technical limitations in our experimental system currently inhibit the formation of such states. In the second experiment we introduce a novel gate scheme for quantum computation using trapped Rydberg ions, initial results demonstrating the feasibility of the gate scheme are presented and future plans for this work are summarized. For the final experiment we investigate the effects of an electric quadrupole field interacting with a single ion to second and higher orders. We observe resonance shifts for the Rydberg excitation and the presence of sidebands due to the interaction when performing spectral scans. These observations show good agreement when compared with theoretical models. Finally a new technique for performing coherent spectroscopy of Ryberg states is demonstrated.