Neodymium, one of the more critically scarce rare earth metals, is often used in sustainable technologies. In this study, we investigate the potential contribution of neodymium recycling to reducing scarcity in supply, with a case study on computer hard disk drives (HDDs). We first review the literature on neodymium production and recycling potential. From this review, we find that recycling of computer HDDs is currently the most feasible pathway toward large-scale recycling of neodymium, even though HDDs do not represent the largest application of neodymium. We then use a combination of dynamic modeling and empirical experiments to conclude that within the application of NdFeB magnets for HDDs, the potential for loop-closing is significant: up to 57% in 2017. However, compared to the total NdFeB production capacity, the recovery potential from HDDs is relatively small (in the 1-3% range). The distributed nature of neodymium poses a significant challenge for recycling of neodymium.