This paper considers the digital transformation of museums and, particularly, the challenges museum professionals face today in the implementation of digital practices. The exploration of the challenges that museum professionals need to address, and the values associated with the “digital” are critical in the context of current and rapid sociocultural and technological changes. This paper reviews a diverse typology of resources—including project reports and deliverables, qualitative and quantitative surveys, academic articles, edited volumes, and chapters—relevant to the implementation of digital practices in the “backstage of museums.” This essay will show that, although digital technologies have acquired a normative presence, organisational and technical challenges in the “backstage” of museums pose systemic problems in their digital transformation. These are systemic problems related to skills and knowledge, and human and financial resource deficits, which result in museum professionals exerting constant effort to keep up with the rapid changes in digital technologies with limited resources at hand and the risks of technological obsolescence and abandonment always present. Situated within the emerging literature advocating for a holistic, ethical, and sustainable digital transformation of museums, this paper draws attention to the implications of the digitalisation of museums in the transition to a responsible and sustainable digital future in a European context. It argues that a relational understanding of sustainability and ethics can be a pivotal first step towards the formation of a digitally purposeful museum in the post-digital era.