The present International Celestial Reference Frame (ICRF), the ICRF-3 is based on a catalogue of 4536 quasar positions obtained from Very Long Baseline Interferometry (VLBI) radio measurements. This radio frame is crucial for many applications, from measurements of Earth’s orientation in space to spacecraft navigation and measurements of sea-level rise. However, the deficit in ICRF source density in the South and lack of dedicated imaging campaigns in the South, to monitor structural changes, remain a big concern. These ICRF sources can exhibit spatially extended emission structures that can have a significant effect on astrometric VLBI measurements. The Celestial Reference Frame Deep South (CRDS) is a dedicated astrometric VLBI programme to observe Southern ICRF sources on a regular basis. In an effort to improve the situation in the South, these CRDS sessions have recently been optimized for VLBI imaging. In this thesis, I present VLBI images and source structure analysis results for southern ICRF sources observed in four of these CRDS sessions. For some of these sources, I present the very first high-resolution radio images. I also present results from source structure analysis and a corresponding assessment of astrometric quality, and I also present results from efforts to increase the ICRF source density in the South. / Mathematical Sciences / Ph. D. (Astronomy)