In this thesis I discuss the characterisation and development of sources of both linearly and radially polarised terahertz radiation, and present the results of using linearly polarised terahertz radiation to investigate the carrier dynamics in GaN semiconductor systems. Linearly polarised terahertz radiation was generated by large area and interdigitated photoconductive antennas (PCAs) and through four-wave rectification in an air plasma. A comparison of the electric fields, the bandwidths, dynamic range and signal-to-noise ratio was made between the three sources, with comments made regarding the suitability of these sources for use in spectroscopic measurements. In order to investigate the cause of efficiency droop in InGaN/GaN multiple quantum well (MQW) structures, a combination of time-integrated photoluminescence spectroscopy and time-resolved terahertz and photoluminescence spectroscopies were used. The results of these investigations are presented with the aim to shed light on the mechanism behind efficiency droop, and provide strong evidence that it is the saturation of the localised hole states that contribute to the efficiency droop in these samples. Radially polarised radiation has been observed to have an enhanced longitudinally polarised component, when compared to linearly polarised radiation. Two radially polarised terahertz sources were characterised, a large area radial PCA and a radial interdigitated structure, the results of which are presented here. The longitudinal electric field component was found to have amplitudes of 2.2 kVcm-1 and 3.5 kVcm-1 for the large area and the interdigitated radial PCAs respectively. The bandwidth, dynamic range and signal-to-noise ratio of both devices are also discussed, alongside the scalability of the interdigitated structure.