Very Long Baseline Radio Interferometry is one of the most recently developed and potentially most useful geodetic measuring techniques. The high accuracy which it can achieve over great distances makes it ideally suited. for studies of many interesting geodetic and geophysical phenomena. The major asset of the system is that, unlike the majority of other accurate techniques, all measurements are independent of the Earth's gravity field. This thesis contains details of the basic theory of the VLBI technique and describes a model which has been developed to analyse data from the system. This is followed by a description of the application of the variation of co-ordinates method to the adjustment of VLBI observations and details the conditions and restrictions to be applied to the adjustment process. The basic procedure and equipment required to make the observations is described and details are given of the Nottingham University Long Baseline Interferometry Programs (NULBIP) which have been developed to perform the data analysis. Data has been obtained and analysed from two independent sets of observations using two different VLBI observing systems. The Canadian system has been used for observations using the three antenna array comprising the Chilbolton Observatory, England, the Algonquin Radio Observatory, Canada, and the Owens Valley Radio Observatory, U. S. A. Observations have also been processed from the Haystack-Goldstone baseline in the U. S. A., observed using the NRAO Mk I VLBI system. The software which has been developed has been tested by comparison with independently derived results on these baselines. The analysis of all the data has shown the VLBI method to be a highly accurate technique capable of measuring intercontinental distances with sub-metre accuracy. The results have indicated the many potential uses of VLBI in geodetic and geophysical research, the major ones of which have been described. The magnitude of systematic scale and orientation errors inherent in the Navy Navigation Satellite System (otherwise known as the TRANSIT system) have been measured by comparing these VLBI results with satellite-Doppler results derived from observations made near the radio telescopes.