I will first present some of the observational and theoretical evidence for the morphological and dynamical transformation of galaxies through cosmic time. This transformation is thought to result from the complex interplay between the hierarchical merging of dark matter halos and baryonic processes. I will first show that measuring and contrasting the dynamical state of galaxies using gas and stars in and beyond the local Universe is an important test of our understanding of structure formation. I will discuss barriers to the accurate measurement of dynamical evolution in galaxies and suggest possible solutions. In particular, strategies for mitigating the 'progenitor bias' in observational surveys will be outlined. I will discuss some recent results from the Middle-Ages Galaxy Properties with Integral field spectroscopy (MAGPI) Survey, a VLT/MUSE large programme designed to replicate the depth and spatial resolution of local integral field spectroscopy surveys at intermediate redshift (z~0.3). MAGPI provides a 3D snapshot of the dynamical state of both the ionised gas and stars in galaxies at the highest feasible lookback time.