This paper studies the recent evolutions in digital cultural mediation for museums. It aims to show the convergence of recent socio-technological trends and their social appropriation by museums towards the building of an " open museum " based on the paradigm of collaboration and open access to culture. In the last fifteen years, museums developed policies to make digital cultural resources available. To facilitate the dissemination and circulation of cultural contents, they adopted the media habits of their audience by relying on electronic artefacts and digital data. They began with local indoor installations, then extended them to websites and social networks and finally went digitally mobile with specific apps. This innovative digital communicational policy blurs boundaries between in-situ physical museums and their digital resources. Museum contents are displayed on external platforms developed by industrial stakeholders whose core business was not initially the cultural field. This new configuration allows individual access to cultural content inside and outside the museum by combining the discovery of physical locations and digital resources. In this perspective, we investigated cultural Linked Open Data, in particular the opportunities offered by the social construction of an inter-museum cultural space leading to free circulation of knowledge. We showed that the notion of museum is being extended to include digital social networks, digital mobility and cultural Linked Open Data. This conception of a museum extending beyond its physical space to digital spaces is what could be called an "open museum." Our approach is based on three studies: a) a qualitative analysis of a corpus of professional publications by American and European museums during years 2012-2014; b) five case studies based on interviews with professionals from five American museums; c) one specific example, " Musée d'Histoire de Marseille " in France, in which one of the authors was involved.