The strongest fibres available today are carbon-based, made from carbon nanotubes (CNTs) or reduced graphene oxide flakes (RGOFs). Carbon fibres (CFs) were first developed half a century ago. Control of the thermal, chemical and mechanical processing allows obtaining desired combination of structure, strength and stiffness. In practical use, CFs are typically incorporated into larger scale systems that require multi-scale characterisation. In the present study we considered an aerospace composite consisting of titanium alloy matrix reinforced with unidirectional silicon carbide fibres with carbon monofilament core. By combining synchrotron-based imaging and nano-focused X-ray beam scattering with Focused Ion Beam stress evaluation, we construct detailed maps of structure and strain inside this material. Eigenstrain modelling was used to reconstruct the full residual strain state within the fibre cross-section. The joined-up experimental and theoretical approach allows extracting information about fibre structure down to the nanoscale, developing insight into its processing history, and revealing the existence of significant residual strains that have a strong effect on the performance of CFs in service.