In this dissertation, we study methods for improving the routing performance of computer communication networks in dynamic environments. The dynamic environments we considered in this work include both network topology changes and traffic demand changes. In the first part, We propose a novel fast rerouting scheme for link state routing protocols. Link state routing protocols are widely used by todayAcA?A?s ISPs on their backbone networks. The global update based rerouting of link state protocols usually takes seconds to complete which affects real time applications like Voice over IP. In our scheme, usually, only routers directly connected to failed links are involved in rerouting. For other cases, only a small number of neighboring routers are also involved. Since our scheme calculates rerouting paths in advance, rerouting can be done faster than previous reactive approaches. The computation complexity of our scheme is less than previous proactive approaches. In the second part, we study Multihoming Route Control (MRC) that is a technology used by multihomed stub networks recently. By selecting ISPs with better quality, MRC can improve routing performance of stub networks significantly. We first study the stability issue of distributed MRC and propose two methods to avoid possible oscillations of traditional MRC. The first MRC method is based on AcA?A?optimal routingAcA?A?. The idea is to let the stub networks belonging to a same organization coordinate their MRC and thus avoid oscillations. The second method is based on AcA?A?user-optimal routingAcA?A?. The idea is to allow MRC devices to use multiple paths for traffic to one destination network and switch traffic between paths smoothly when path quality or the traffic matrix changes. A third MRC method we propose is for MRC of traffic consisting of TCP flows of different sizes on paths with bottlenecks of limited capacity. Based on analysis of quality characteristics of bottleneck links, we propose a greedy MRC approach that works in small timescales. Simulation results show that the proposed MRC method can greatly improve routing performance for the MRC sites as well as the overall routing performance of all sites in the network.