Over the past two decades, the development of methods for visualizing and analysing specimens digitally, in three and even four dimensions, has transformed the study of living and fossil organisms. However, the initial promise that the widespread application of such methods would facilitate access to the underlying digital data has not been fully achieved. The underlying datasets for many published studies are not readily or freely available, introducing a barrier to verification and reproducibility, and the reuse of data. There is no current agreement or policy on the amount and type of data that should be made available alongside studies that use, and in some cases are wholly reliant on, digital morphology. Here, we propose a set of recommendations for minimum standards and additional best practice for three-dimensional digital data publication, and review the issues around data storage, management and accessibility.