The imaging of catalysts and other functional materials under reaction conditions has advanced significantly in recent years. The combination of the computed tomography (CT) approach with methods such as X-ray diffraction (XRD), X-ray fluorescence (XRF) and X-ray absorption near-edge spectroscopy (XANES) now enables local chemical and physical state information to be extracted from within the interiors of intact materials which are, by accident or design, inhomogeneous. In this work, we follow the phase evolution during the initial reduction step(s) to form Co metal, for Co-containing particles employed as Fischer-Tropsch synthesis (FTS) catalysts; firstly, working at small length scales (approx. micrometre spatial resolution), a combination of sample size and density allows for transmission of comparatively low energy signals enabling the recording of 'multimodal' tomography, i.e. simultaneous XRF-CT, XANES-CT and XRD-CT. Subsequently, we show high-energy XRD-CT can be employed to reveal extent of reduction and uniformity of crystallite size on millimetre-sized TiO2 trilobes. In both studies, the CoO phase is seen to persist or else evolve under particular operating conditions and we speculate as to why this is observed.This article is part of a discussion meeting issue 'Providing sustainable catalytic solutions for a rapidly changing world'.