Since its birth in the early seventeenth century, the press has played a prominent role in the political and social life of France. Over the two last decades, the economic and even cultural pillars on which the press ecosystem is built has been challenged by the growing use of digital technologies, and by the increasing role of the Internet as a way to distribute and access information. Heritage libraries need to address the accelerating shift from analogue to digital in order to maintain the continuity of their objectives and of their missions. Many aspects need to be taken into account: legal, scientific, technical, economic and organizational issues have to be identified and addressed. This paper looks at the example of the National Library of France (Bibliothèque nationale de France or BnF), and at the way it has dealt with collecting newspapers in digital form. During the ten last years, the BnF has launched several experiments, testing different approaches, with varying degrees of success: - Direct deposit of electronic publications on physical media (CDs and DVDs) or through FTP. - Fully automated web harvesting. Since December 2010, almost 100 news websites (national and daily newspapers, pure players, news portals...) are collected on a daily basis. -Web harvesting through agreements with producers.