The present survey seeks to contribute to the existing discussion about the changing of current Public Protection and Disaster Relief (PPDR) networks (TETRA, TETRAPOL, P25, and DMR) to commercial cellular networks (4G and 5G). The availability and robustness of these commercial networks are challenging current PPDR networks and creating opportunities for a successful transition of existing systems to commercial cellular networks. Specifically, 5G networks aim to support a massive number of heterogeneous devices while providing ultra-reliable low latency communications, higher mobility, and the capability of customised support of applications via network slicing, thus providing a natural contribution to mission critical systems. This survey details the essential mission requirements of security of PPDR systems, describes the state of the art of the most used technologies and discusses their evolution to 4G and 5G cellular networks. Furthermore, it analyses future research directions that may contribute to a successful transition of current systems to the newer cellular networks.