Museums play an important role in tourist flows, especially in cities that are famous for their cultural heritage. To valorize their role, these cultural institutions should open themselves to visitors as vectors of social, educational, and entertainment values. In particular, museums need to reinvent how they transmit information about their collections and how they engage visitors, keeping in mind the opportunities triggered by digitalization. Digital technologies could in fact be a powerful tool to assist in adopting a visitor-oriented approach and to stimulate a two-way communication. This article aims to analyze the extent of digitalization that should be integrated in museums' communication strategies, and to recognize the logics hindering digital transformation in cultural heritage strategic management. We developed an exploratory case study, focused on museums in Turin, Italy, gathering online data through institutional reports, museum websites, and social media, as well as onsite data mainly from semistructured interviews with museum managers. The research shows that most of the interviewees understand the strategic role of digitalization for museum development; however, the level of digital readiness remains low. Alongside the well-known systemic financial deficit of cultural institutions, there are other critical factors that hinder the integration of digitalization processes in the cultural heritage management. Common barriers include the presence of institutional pressures, and the lack of organizational and managerial coordination between different departments and functions that should be involved in the development of digital strategies and their integration in the strategic planning systems of museums. This research offers insights to tackle these challenges, allowing museums to compete in the international context of the cultural and heritage tourism.