Mobile data traffic has been rapidly increasing over the last few years. To accommodate for such an ever–growing traffic demand, mobile network operators are required to perform costly network upgrades. Cell size reduction and network virtualization are known to be two of the most effective ways to increase capacity and lower the cost to deploy and operate future mobile networks. This PhD thesis will study the trade–offs associated with the different approaches to small cell virtualization in terms of the point at which base stations operations are decomposed into physical and virtual. Different functional splits will be compared using mathematical optimization tools (e.g., Integer Linear Programming) while novel heuristics will be devised in order to tackle problems of practical size. Finally, selected results will be empirically evaluated over the 5G-EmPOWER testbed deployed at CREATE-NET premises.