Traditionally, emergency communications between citizens and public authorities relied on legacy telecommunication technologies unable to cope with the agile, rich-media-content communications that mobile users are already using. This is due to the lack of harmonization and interoperable IP-based networking solutions. With the operators currently migrating to broadband IP infrastructures, emergency systems also need to follow this path and adapt their emergency communication platforms to fulfill next generation emergency services regulatory requirements. This becomes even more evident in light of the forthcoming 5G networks, which are envisioned to support an amalgam of diverse applications and services with heterogeneous performance requirements, including mission-critical IoT communication, massive machine-type communication, and gigabit mobile connectivity. Emergency service operators face an enormous challenge in order to synchronize their model of operation with the 5G paradigm. This article studies the challenges that next generation emergency services need to overcome in order to fulfill the requirements for rich-content, real-time, location-specific communications. The concept for next generation emergency communications as described in the project EMYNOS is presented, along with a vision of how this concept can fulfill the 5G requirements for ultra-reliable and ultra-low-latency emergency communications.