The Internet has become the standard infrastructure for all kinds of communications. At the same time, the emergence of cloud computing and web services has significantly strengthened requirements for the Internet to display greater robustness to disruptions and higher flexibility to support emerging applications. As hardware components are increasingly reliable and capable of handling a growing volume of Internet traffic, routing has not only become the biggest contributor to problems such as performance degradations and failures, but it also affects network flexibility and its ability to provide services. Furthermore, because of growing Internet penetration, routing is playing an ever greater role in shaping the scalability challenges that need to be met to enable the continued expansion of the Internet. The goal of the thesis is, therefore, to explore the role of routing in building a "Sustainable Internet" that can satisfy the future needs of communications along the dimensions of performance, flexibility, robustness, and scalability. The thesis presents a comprehensive approach to building a sustainable Internet from a routing perspective, and solves the following three challenges. The first challenge stems from the fact that IP networks need to support a wide variety of applications with diverse properties and requirements. It is therefore important to understand how routing can be designed and optimized to flexibly support diverse applications in IP networks with performance guarantees. However, flexibility without robustness to disruptions is of limited benefits, because IP networks face the daunting task of handling increasingly diverse traffic that is displaying a growing intolerance to disruptions. As a result, the second challenge is to seek routing solutions for balancing flexibility and robustness in IP networks. Furthermore, IP networks also need routing robustness for their Internet connectivity. Although it can be achieved by multi-homing, this has a global effect on the expansion of core Internet routing tables and ultimately impacts on the scalability of the Internet routing system. Thus, the third challenge is to explore solutions for controlling the growth of core Internet routing tables while balancing the needs of robustness for the Internet connectivity of IP networks.