This thesis considers the radio resource management (RRM) of advanced wireless communication systems. With the emerging of more advanced and more complicated systems, such as cognitive radio, nodes with energy harvesting capacities (green communications), and the application of Multiple-Input Multiple-Output (MIMO) technology, RRM problems introduce more difficulties and challenges to optimize system performances. Due to specific structure of communication systems, water-filling (WF) plays an important role in RRM. This thesis introduces the fundamental theory and development of WF algorithm. The proposed Geometric Water-Filling (GWF) is presented and compared with the conventional WF algorithms. It can break through the limitations of the conventional WF to solve the more complicated optimization problems in the advanced wireless communication systems. For the application of the proposed GWF to solve the RRM problems in the advanced MIMO communication systems, cognitive radio communication systems, green communication systems and the “dual problems”, which are the sum power minimization problems, of the throughput maximization problems is investigated in this thesis. Efficient algorithms are presented to achieve the optimal resource allocation.