Real-time applications such as Voice-over-IP, streaming multimedia, multi-player gaming and pervasive virtual environments account for a massive proportion of the Internet economy. These services consist of traffic flows which have requirements in terms of bandwidth, loss, delay and jitter in order to provide a usable experience to an end-user. Current approaches to providing specialised service for real-time traffic involve queueing mechanisms, resource reservation, traffic engineering or admission control. These strategies all either have scalability issues, do not work in an end-to-end fashion, or are manual and off-line in nature. This dissertation describes and evaluates new approaches for on-line routing of real-time flows. Our framework for this work is the Cognitive Packet Network (CPN), a self-aware routing protocol which uses a user-directed, goal-based reinforcement learning technique to route flows according to the metrics which most impact their performance. We first compare CPN with an industry standard routing protocol (OSPF), demonstrating through experiments with multiple flows carrying real-time traffic that CPN can quickly converge to the optimal route in a network, and that the speed with which this occurs is proportional to its exploratory overhead. This work is the first. to explore CPN's performance with multiple flows competing for the available network resources. This leads to our second contribution where we investigate the impact of competition among selfish network flows and the potential for routing oscillations. We demonstrate that. these oscillations can harm overall QoS, and develop methods for eliminating them without sacrificing the benefits of CPN's exploratory nature. Towards supporting applications which have diverse Quality of Service (QoS) requirements, we develop goals in terms of two metrics (loss and delay) and show that CPN can adaptively learn paths in terms of each; in cases of moderate congestion it can decrease network losses by up to a factor of 10. Finally, we show that by using an overlay network, the benefits of CPN routing can be introduced into existing networks with low overhead and without modifying their underlying routing mechanisms.