The Italian Tsunami Alert Center based at the Istituto Nazionale di Geofisica e Vulcanologia (CAT‐INGV) has been monitoring the Mediterranean seismicity in the past 8 yr to get fast and reliable information for seismically induced tsunami warnings. CAT‐INGV is a tsunami service provider in charge of monitoring the seismicity of the Mediterranean Sea and of alerting Intergovernmental Oceanographic Commission (IOC)/UNESCO subscriber Member States and the Italian Department of Civil Protection of a potentially impending tsunami, in the framework of the Tsunami Warning and Mitigation System in the North‐eastern Atlantic, the Mediterranean and connected seas (NEAMTWS). CAT‐INGV started operating in 2013 and became operational in October 2016. Here, after describing the NEAMTWS in the framework of the global effort coordinated by IOC/UNESCO, we focus on the tsunami hazard in the Mediterranean Sea. We then describe CAT‐INGV mandate, functioning, and operational procedures. Furthermore, the article discusses the lessons learned from past events occurring in the Mediterranean Sea, such as the Kos‐Bodrum in 2017 ( 6.6) and the Samos‐Izmir in 2020 ( 7.0) earthquakes, which generated moderately damaging tsunamis. Based on these lessons, we discuss some potential improvements for the CAT‐INGV and the NEAMTWS, including better seismic and sea level instrumental coverage. We emphasize the need for tsunami risk awareness raising, better preparation, and full implementation of the tsunami warning “last‐mile” to foster the creation of a more integrated, interoperable, and sustainable risk reduction framework. If we aim to be better prepared for the next tsunami, these important challenges should be prioritized in the agenda of the IOC/UNESCO Member States and the European Commission.