Pacing the way towards 5G has lead researchers and industry in the direction of centralized processing known from Cloud-Radio Access Networks (C-RAN). In C-RAN research, a variety of different functional splits is presented by different names and focusing on different directions. The functional split determines how many Base Station (BS) functions to leave locally, close to the user, with the benefit of relaxing fronthaul network bitrate and delay requirements, and how many functions to centralize with the possibility of achieving greater processing benefits. This work presents for the first time a comprehensive overview systematizing the different work directions for both research and industry, while providing a detailed description of each functional split option and an assessment of the advantages and disadvantages. This work gives an overview of where the most effort has been directed in terms of functional splits, and where there is room for further studies. The standardization currently taking place is also considered and mapped into the research directions. It is investigated how the fronthaul network will be affected by the choice of functional split, both in terms of bitrates and latency, and as the different functional splits provide different advantages and disadvantages, the option of flexible functional splits is also looked into.