The rise of postcolonial theories in the 1970s did not yield much influence in the then practice of humanities computing, but following the mass-scale digitisations of cultural heritage materials over the past thirty years questions of Indigenous agency and the colonial roots of the digital cultural record have become more urgent than ever. This thesis operates within the area of postcolonial digital humanities and seeks to explore three questions. The first regards the socioethical concerns associated with the digitisation of Indigenous cultural heritage materials originating in Oceania, a geographic region which is peripheral on digital humanities maps but at the same time paradigmatic for exploration due to its cultural, political and linguistic diversity and multiple histories of colonial plundering. The second question investigates the extent to which global cultural heritage institutions digitise collections originating in Oceania in a culturally responsive manner, whereas the third focuses on the actions that digitising institutions can take in order to improve their websites from a decolonising perspective. The analysis that has been conducted on relevant literature and digitisation websites has resulted in an outline of theoretical concerns that should be taken into consideration prior to digitisation, as well as an assessment of existing digitisation activities and recommendations for improvement.