The fifth-generation (5G) wireless cellular system, which would be deployed by 2020, is expected to deliver significantly higher capacity and better network performance compared to those of the current fourth-generation (4G) system. Specifically, it is predicted that tens of billions of wireless devices will be connected to the wireless network over the next few years, which results in an exponential explosion of mobile data traffic. Therefore, more advanced wireless architecture, as well as radical and innovative access technologies, must be proposed to meet this urgent increasing growth of mobile data and connectivity requirements in the coming years. Toward this end, two important wireless cellular architectures, namely wireless heterogeneous networks (HetNets) based on the dense deployment of small cells and the cloud radio access networks (C-RANs) have been proposed and actively studied by both academic and industry communities. Besides enabling a lot of advantages in increasing network coverage as well as end-to-end system throughput, these two novel network architectures have also raised some novel technical challenges and opened exciting research areas for further research. Motivated by the aforementioned technical challenges, the general objective of this Ph.D. research is to develop efficient radio resource allocation and interference management algorithms for the future high-speed wireless cellular networks. In particular, we have developed various efficient resource allocation algorithms for reducing the transmission power and increasing the end-to-end network throughput for both HetNets and C-RANs. Furthermore, extensive numerical results are presented to gain further insights and to evaluate the performance of our resource allocation designs.