Intermetallic titanium aluminides based on the ordered ¿-TiAl phase provide promising properties for modern lightweight high-temperature applications. In particular, they combine a low density of roughly 4 g·cm-3 with a high specific Young¿s modulus and strength at elevated temperatures, excellent creep properties, and good oxidation and burn resistance. Innovative materials of this kind are urgently required, since only their implementation can secure the fulfilment of current and future regulatory requirements for road and air traffic in terms of fuel efficiency, environmental emissions, and noise. Yet, to fully exploit the potential of ¿-TiAl based alloys, ensure their safety for application, and reduce production cost, further fundamental investigations into this class of materials are critically needed. As materials systems grow increasingly complex, these investigations often require advanced characterisation methods. This work employed state-of-the-art synchrotron X-ray diffraction and scattering techniques as well as various complementary methods to explore research questions that are hardly accessible by means of conventional characterisation techniques. For example, novel sheets based on the ß-solidifying TNM alloy of a nominal chemical composition of Ti¿43.5Al¿4Nb¿1Mo¿0.1B (at.-%) were characterised. The analysis of the evolution of microstructure and texture during hot rolling, ensuing processing, and heat treatments allowed establishing a fundamental understanding of the processes prevailing in the TNM alloy during sheet manufacturing. This knowledge can be applied to create TNM sheets with weak textures and balanced, isotropic mechanical properties. The room temperature deformation behaviour of the TNM sheets, which is crucial for their applicability, handling, and safety aspects, as well as the previously unknown role of the ßo-TiAl phase with regard to load partitioning were elucidated by means of in situ tensile tests. Finally, in situ small-angle X-ray scattering and high-energy X-ray diffraction were combined to explore opportunities for microstructural design based on the ß/ßo phase in ternary Ti¿Al¿Mo model alloys. Specifically, the early growth stages of ¿ precipitates from a supersaturated ßo matrix in the Ti¿44Al¿7Mo (at.-%) alloy were studied for the first time, as such refined microstructures offer promising mechanical properties for advanced structural applications. Based on the establishment of a profound understanding of the mechanisms prevailing in ¿-TiAl based alloys under various conditions of fundamental or technological relevance, significant improvements in the design and processing can be effected.