The Earth’s inner core provides unique insights into processes that are occurring deep within our Earth today, as well as processes that occurred in the past. The seismic structure of the inner core is complex, and is dominated by anisotropic and isotropic differences between the Eastern and Western ‘hemispheres’ of the inner core. Recent geodynamical models suggest that this hemispherical dichotomy can be explained by a fast translation of the inner core. In these models one side of the inner core is freezing, while the other side is melting, leading to the development of different seismic properties on either side of the inner core. A simple translating model of the inner core, however, does not seem to easily explain all of the seismically observed features, including the innermost inner core; the observed sharp lateral gradient in seismic properties between the two hemispheres; and a complex hemispherical and radial dependence of anisotropy, attenuation, and scattering in the uppermost inner core. We explore the compatibility of geodynamic models of a translating inner core with seismic observations. Using a relatively simple set of translation models we map the age of material in the inner core and apply mineral physics models for the evolution of grain size to estimate likely changes in seismic properties throughout the inner core. We then compare these predictions to the observations of seismic studies that target two regions that are highly sensitive to the translation of the inner core: the boundary between the two hemispheres and the regions of freezing and melting at the inner core boundary. To constrain the sharpness of the boundary between the two hemispheres of the inner core we collate a data set of PKiKP-PKIKP, PKP-PKIKP and P”_P”_bc-P”_P”_df differential travel times consisting of paths that sample the core near to the proposed hemisphere boundaries. This combination of body wave data samples a range of depths (and consequently ages) in the inner core, and provides an insight into the nature of hemispheres and their compatibility with our predictions for models of a translating inner core. Additionally, we investigate the structure at the base of the outer core and the inner core boundary by analyzing PKP-Cdiff waves. The search for observable PKP-Cdiff is particularly concentrated in regions that are predicted to be actively freezing and melting, and spans a range of frequencies, allowing us to fully investigate any regional differences around the inner core boundary that may result from the translation of the inner core.