Denial of service (DoS) attacks and distributed denial of service (DDoS) attacks are probably the most ferocious threats in the Internet, resulting in tremendous economic and social implications/impacts on our daily lives that are increasingly depending on the well-being of the Internet. How to mitigate these attacks effectively and efficiently has become an active research area. The critical issues here include (1) IP spoofing, i.e., forged source IP addresses are routinely employed to conceal the identities of the attack sources and deter the efforts of detection, defense, and tracing; (2) the distributed nature, that is, hundreds or thousands of compromised hosts are orchestrated to attack the victim synchronously. Other related issues are scalability, lack of incentives to deploy a new scheme, and the effectiveness under partial deployment. This dissertation investigates and proposes effective schemes to mitigate DDoS attacks. It is comprised of three parts. The first part introduces the classification of DDoS attacks and the evaluation of previous schemes. The second part presents the proposed IP traceback scheme, namely, autonomous system-based edge marking (ASEM). ASEM enhances probabilistic packet marking (PPM) in several aspects: (1) ASEM is capable of addressing large-scale DDoS attacks efficiently; (2) ASEM is capable of handling spoofed marking from the attacker and spurious marking incurred by subverted routers, which is a unique and critical feature; (3) ASEM can significantly reduce the number of marked packets required for path reconstruction and suppress false positives as well. The third part presents the proposed DDoS defense mechanisms, including the four-color-theorem based path marking, and a comprehensive framework for DDoS defense. The salient features of the framework include (1) it is designed to tackle a wide spectrum of DDoS attacks rather than a specified one, and (2) it can differentiate malicious traffic from normal ones. The receiver-center design avoids several related issues such as scalability, and lack of incentives to deploy a new scheme. Finally, conclusions are drawn and future works are discussed. [The dissertation citations contained here are published with the permission of ProQuest LLC. Further reproduction is prohibited without permission. Copies of dissertations may be obtained by Telephone (800) 1-800-521-0600. Web page: http://www.proquest.com/en-US/products/dissertations/individuals.shtml.]