The range of applications and services which can be successfully deployed in packet-switched networks such as the Internet is limited when the network does nor provide Quality of Service (QoS). This is the typical situation in today's Internet. A key aspect in providing QoS support is the requirement for an optimised and intelligent mapping of customer traffic flows onto a physical network topology. The problem of selecting such paths is the task of QoS routing QoS routing algorithms are intrinsically complex and need careful study before being implemented in real networks. Our aim is to address some of the challenges present m the deployment of QoS routing methods. This thesis considers a number of practical limitations of existing QoS routing algorithms and presents solutions to the problems identified. Many QoS routing algorithms are inherently unstable and induce traffic fluctuations in the network. We describe two new routing algorithms which address this problem The first method - ALCFRA (Adaptive Link Cost Function Routing Algorithm) - can be used in networks with sparse connectivity, while the second algorithm - CAR (Connectivity Aware Routing) - is designed to work well in other network topologies. We also describe how to ensure co-operative interaction of the routing algorithms in multiple domains when hierarchial routing is used and also present a solution to the problems of how to provide QoS support m a network where not all nodes are QoS-aware. Our solutions are supported by extensive simulations over a wide range of network topologies and their performance is compared to existing algorithms. It is shown that our solutions advance the state of the art in QoS routing and facilitate the deployment of QoS support in tomorrow's Internet.