Mobile telecommunication networks have become widespread in the last almost forty years, and nowadays life is unimaginable without them. In my thesis, first of all, I present a short overview of the development of mobile communication networks so far, then I present the expectations set against the new, fifth generation network, which is still under development, and expected to start to roll out shortly, based on information from equipment manufacturers and the standardization bodies. Then I present the current network variations and the improvements made to the core network. I pay special attention to the problem of network slices: I present the workings of virtual network functions, placed in data centers, and the problem of their placement, and I attempt to present a possible solution to this problem, with a crafted algorithm. I detail how the algorithm works, and the results achieved by it. Finally, I present the timeframe when these networks can be expected to be deployed and spread, and what kind of enhancements could be made to my work in the future.