The technologies developed for the next generation of cellular networks (i.e., 5G) are potential enablers for future Public Safety Communication (PSC) systems. These will indeed need advanced communication techniques, capable of providing real-time, lowlatency and reliable interactions in different scenarios (vehicular, aerial, unmanned) and different network architectures. There is great interest in the millimeter wave (mmWave) band and in general in the spectrum above 6 GHz, since the bandwidth that can be allocated at these frequencies is much higher compared to the traditional (and congested) sub-6 GHz bands. This would enable orders of magnitude greater throughput and low latency, which could be used for example to stream high definition video or virtual/augmented reality data to first responders or for the remote control of autonomous robots. In this paper we illustrate both the potential of mmWave communications for PSC (also with a typical use case) and the issues that must be solved before this technology can be reliably adopted and mmWave PSC networks become a reality.