Social media have sparked increasing appeal for improving emergency management. Many have advocated the use of Social Media for Emergency Management (SMEM) to disseminate early warnings. Resorting to the massive but unstructured inVoluntary Geographic Information (iVGI) from social media during disaster response phase has been encouraged for rapid assessment, location and mapping of people and events, for monitoring the expressed needs and for observing human behavior in crisis dynamics. SMEM encompasses top-down – public information, community engagement – bottom-up – situational awareness, urgent needs collection – and many-to-many information flows – allowing a large number of users to communicate with each other simultaneously in real-time. However, operationalizing social media data in real-time during emergency situations might not be as practical as ex post facto retrospective analyses usually suggest. We question the use of SMEM and the unchallenged expectations that they allow for a faster and more widespread dissemination of early warnings, more citizens involvement and offer a richer and more contextualized crowdsourced feedback than classic emergency channels. We analyze the usefulness of geotagged information to monitor the unfolding of a crisis in real time and to accurately detect events and map people. We also question if the use of social media for emergency management is conditioned by local context and governance, by making a comparison between European countries. We offer a critical review of the literature, an SMEM analytical framework, and then empirical work based on large Twitter datasets collected from three different terror attacks in Europe: the Paris attacks in November 2015, the Brussels attacks in March 2016, and the Nice attack in July 2016. The results reveal important delays in warnings and information sharing, and that the press overshadows official accounts. Moreover, first-hand information is often too scattered, too thinly geotagged, and too late to be reliably used during emergency situations.