There are approximately 1.5 billion specimens kept in European Natural History Collections. The mission for the Distributed System of Scientific Collections (DiSSCo) is to unite all these specimens into a one-stop e-science infrastructure of digital specimens. This is a monumental digitisation task and criteria for how to prioritise this effort are, therefore, crucial for the success of the project. In this report, we have reviewed the literature and designed and conducted surveys of the digitisation plans and criteria used by DiSSCo Partners to understand the prioritisation criteria used in the digitisation of natural history collections. As an attempt to provide some guidance for the digitisation of specimens, we suggest that an organisation (e.g. DiSSCo or an individual institution) that is planning to digitise natural history collections considers four categories of prioritisation criteria: Relevance, Data quality, Cost and Feasibility.