This paper aims at highlighting how interest in the issues of web and social media archiving and preservation has grown enormously, in parallel with the awareness of the importance of these ‘resources’ as privileged sources for reconstructing the history of our era. How will the historians of the future be able to reconstruct the historical period we are living through if memory institutions are not able to archive and preserve the websites and social media of institutions, public bodies, parties, associations, government bodies, political figures, and famous people in general, given that everything is now conveyed through these channels? The fragility of the web, then, would require immediate action and the launch of ‘web and social media archiving’ initiatives without delay, on pain of the disappearance of all that has been made available online in recent years, but on this point the situation in Italy - with a few exceptions - appears to lag far behind other European countries and enormously behind the Anglo-Saxon countries. There is therefore an urgent need to launch initiatives to raise awareness on these issues and to train the skills and professionalism required to conduct web and social media archiving and preservation projects.