Many animals’ lives, both in the wild and in captivity, are now greatly influenced by human activities. As a result there are many opportunities for human–animal interactions (HAIs), leading to the establishment of human–animal relationships (HARs). In some cases these can result in strong emotional attachments, human–animal bonds (HABs). The study of these constitutes the subject of Anthrozoology. In this chapter we attempt to define these terms in a way that is applicable across all of the different contexts in which humans and animals come into contact. These relationships can have far-reaching consequences, not only for the individual animals and people involved in the interactions, but also for animal populations and human society more generally, so there are many reasons why we should care and be concerned with them. This chapter introduces some of these areas of concern and their relevance to the different contexts, which are explored in subsequent chapters.