The volume of streaming media content has surged on the Internet in recent years. In parallel with the technological advancement in wireless and third generation (3G) networks, more and more Internet users today are turning to their mobile devices, such as smart phones or PDAs, to access the Internet stream content. However, when compared with desktops, mobile devices normally have different display sizes, color depths, bandwidth capacities, CPU speeds, or battery capacities, which are termed Multiple Dimensional Heterogeneity (MDH). Due to the MDH problem, these mobile devices normally cannot directly display the data streamed to desktops. A few solutions based on Multiple Description Coding (MDC) or Scalable Coding (SC) have been proposed, but none of these solutions are practical due to their various limitations. In this dissertation, novel efficient resource management and transcoding schemes are investigated to address the MDH problem in both Internet on-demand and live streaming systems. First, in on-demand streaming systems, meta-data caching is leveraged during the online transcoding to reduce the overall CPU consumption. A model is further constructed to study the tradeoff between the CPU and the storage consumption for different meta- caching schemes under various conditions. Accordingly, an adaptive scheme that always outperforms existing schemes is proposed. Second, in live streaming systems, the idle peer computing cycles are leveraged for efficient online transcoding based on an additional transcoding overlay constructed by participating transcoding peers. This proposed scheme effectively explores the tradeoff between the CPU and the bandwidth resources. Third, in consideration of resource contributions made by heterogeneous devices and their limited available resources, e.g., battery capacity, we propose a dynamic rotation scheme in both streaming and meta-transcoding overlays to balance the resource consumption among different peers, aiming to improve the fairness among peers and the overall system robustness. Fourth, a general theoretical framework is constructed to maximize the resource utilization in heterogeneous streaming systems. Accordingly, a distributed algorithm is proposed to achieve near-optimal performance with acceptable control overhead.