The Internet has become a critical component of our society, but its routing infrastructure, that is in charge of delivering traffic toward different IP address blocks, i.e. IP prefixes, can undergo many types of anomalies. The anomalies can occur at both the global level and the IP prefix level. At the global level, the Internet routing can deviate from its normal state of operation because of disruptive events such as large-scale power outages, undersea cable cuts, or Internet worms, causing what we call an "Internet earthquake." At the IP prefix level, a prefix can experience degraded or completely broken services because of operational malpractice or security attacks; in prefix hijacking, for example, by lying about routing paths an attacker can hijack or intercept traffic toward a prefix at ease. We therefore conduct a series of studies on Internet routing and infrastructure security, including two Internet routing monitoring systems that we have been researching: "Internet Seismograph" that can be used to measure Internet earthquakes, and "Buddyguard" that detects and analyzes prefix-level routing anomalies.