IP addresses are essential resources for communication over the Internet. In IP version 4, an address is represented by 32 bits in the IPv4 header; hence there is a finite pool of roughly 4B addresses available. The Internet now faces a fundamental resource scarcity problem: The exhaustion of the available IPv4 address space. In 2011, the Internet Assigned Numbers Authority (IANA) depleted its pool of available IPv4 addresses. IPv4 scarcity is now reality. In the subsequent years, IPv4 address scarcity has started to put substantial economic pressure on the networks that form the Internet. The pools of available IPv4 addresses are mostly depleted and today network operators have to find new ways to satisfy their ongoing demand for IPv4 addresses. Mitigating IPv4 scarcity is not optional, but mandatory: Networks facing address shortage have to take action in order to be able to accommodate additional subscribers and customers. Thus, if not confronted, IPv4 scarcity has the potential to hinder further growth of the Internet. Addressing is a collective and global effort, and interconnectivity among networks forms the very basis of the Internet. At the same time, the decentralized nature of the Internet and independent decisions by its different stakeholders create a complex and opaque problem space. Different approaches to mitigating IPv4 address scarcity in the short and in the long term exist. The so- lution space includes increasing the utilization of already available IPv4 address resources, introducing IPv4 address multiplexing techniques, incrementally transitioning to IPv6 (but maintaining IPv4 com- patibility), or purchasing IPv4 address space on address markets. Individual network operators make independent decisions on which approach—or combination of approaches—to pursue. Each option has different ramifications, benefits, and consequences for the individual networks and their connected end users. At the same time, the increasing and disparate deployment of different mitigation techniques and the coexistence of two addressing protocols (IPv4 and IPv6) adds heterogeneity to the network and hence changes the overall connectivity and communication structure of the Internet. In spite of the pressing relevance of the topic, we lack a comprehensive understanding of IPv4 address exhaustion and its effects, as well as of the pervasiveness, impact, and ramifications of the different mitigation strategies. This dissertation provides a systematic empirical analysis of the phenomenon of IPv4 address space exhaustion, its effect on the Internet as a whole, and its stakeholders individually. We first provide an empirical lay-of-the-land of the history and the current status of the IPv4 address space and illuminate the interplay between policy and governance decisions and address use. We then develop techniques that allow us to measure the potential, the pervasiveness, and the ramifications of the individual mitigation strategies that network operators may choose to pursue. In particular, we measure global IPv4 address activity patterns, which allows us to both study exhaustion effects on address activity and to assess the potential for increasing the utilization of the IPv4 address space. We develop tools to detect Carrier- Grade NAT (CGN) presence on the Internet at scale, and identify dominant properties of deployed CGN instances and their respective impact. Lastly, we examine aspects of IPv6 adoption, where we measure inter-domain connectivity and traffic carried over IPv4 and IPv6, and interactions between IPv4 and IPv6 traffic in detail, allowing us to pinpoint barriers and challenges for IPv6 adoption. We strive to both illuminate the broader impact of address exhaustion on the Internet and its structure as well as to provide practical insights to support the ongoing process of mitigating address scarcity. Our results can serve as a basis for network operators and policymakers to make informed decisions on how to approach IPv4 address exhaustion. They may also inform future measurement studies and the design of operational systems, which need to adapt to this increasingly complex environment.