Abelian T-duality is a well-known symmetry of String theory for space-times admitting an Abelian isometry. Less well appreciated is the fact these dualities can be generalised to space-times with non-Abelian and fermionic isometries. While these are not full symmetries of String theory, they still are symmetries of the effective String theory action, namely type II supergravity. One long-standing problem with non-Abelian T-duality is the identification of the dual conformal field theory (CFT), a problem that plagues non-Abelian dualities in general. In contrast, fermionic T-duality has been shown to be intimately related to the hidden symmetries seen in scattering amplitudes, though only for the isolated example of maximally supersymmetric super-Yang-Mills in four space-time dimensions. So, this work aims to address both these shortcomings by identifying the dual CFT for non-Abelian T-duality and finding symmetries of scattering amplitudes in other theories that can be accounted for through fermionic T-duality. Furthermore, we will also investigate the phenomenological and cosmological implications of these symmetries.