The existence of parallel imports (PI) raises a number of interesting policy and strategic questions, which are the subject of this survey article. For example, parallel trade is essentially arbitrage within policy-integrated markets of IPR-protected goods, which may have different prices across countries. Thus, we analyze fully two types of price differences that give rise to such arbitrage. First is simple retail-level trade in horizontal markets because consumer prices may differ. Second is the deeper, and more strategic, issue of vertical pricing within the common distribution organization of an original manufacturer selling its goods through wholesale distributors in different markets. This vertical price control problem presents the IPR-holding firm a menu of strategic choices regarding how to compete with PI. Another strategic question is how the existence of PI might affect incentives of IPR holders to invest in research and development (R&D). The global research-based pharmaceutical firms, for example, strongly oppose any relaxation of restrictions against PI of drugs into the United States, arguing that the potential reduction in profits would diminish their ability to innovate. There is a close linkage here with price controls for medicines, which are a key component of national health policies but can give rise to arbitrage through PI. We also discuss the complex economic relationships between PI and other forms of competition policy, or attempts to limit the abuse of market power offered by patents and copyrights. Finally, we review the emerging literature on how policies governing PI may affect international trade agreements.