Liquid hydrogen is a comparatively high volumetric energy density option for storage and transportation. It however typically requires refrigeration to ~20 K, which incurs a substantial energy penalty. An additional contribution to this energy consumption is the required exothermic conversion between ortho- and para-hydrogen spin isomers. To realise this conversion in a practical timeframe, the use of a spin conversion catalyst is required. To this end, available reaction data in the literature for the ortho-para forward and backward reaction for the range of catalysts considered is summarised and reviewed. Furthermore, the application of a range of reaction kinetic expressions to this assembled data is considered. Available conversion data for ortho-para conversion is sparse, particularly in the temperature-pressure range relevant to hydrogen liquefaction processes. This is less the case for the reverse para-ortho conversion, presumably a consequence of these data being experimentally easier to access. It can also be concluded, based on the available conversion data, that there is currently no compelling reason to adopt anything more complex than first-order kinetics during hydrogen ortho-para conversion reactor design. Finally, a case study is executed which quantifies the sensitivity of this design to current reaction kinetic parameter uncertainty. This review highlights the sparsity of experimental conversion data at relevant cryogenic conditions and the need for a more comprehensive and fundamental understanding of the origins of the spin conversion catalyst effect and how it is impacted by various deactivation mechanisms.