The substantive scope of privacy rights is clearly important, and merits sustained scholarly attention and analysis. However, the remedies available for violations of substantive privacy rights will significantly affect the effective reach of such rights and, accordingly, are no less important in assessing the scope and vibrancy of privacy within a jurisdiction than the substantive rights themselves. Robust remedies available to enforce relatively weak privacy laws can greatly enhance the practical legal effects of such laws; going in the other direction, relatively weak remedies can significantly undermine the potential deterrent effect of broadly written substantive privacy rules. The breadth of the remedies available to enforce privacy rights will significantly affect the efficacy of such rights within a particular polity. What is more, significant differences in remedial schemes can and will exacerbate the conflict of laws problems that currently vex domestic privacy regulators around the globe. To provide one particularly salient example, a recent trend has emerged of national courts issuing global injunctions that require web search engines to deindex content not only within the issuing court’s own jurisdiction, but everywhere else the search engine operates as well. The argument in favour of global injunctions is easy enough to make – if information that violates local law is available anywhere, it is arguably available everywhere. However, the issuance of global injunctions creates a conflict of laws nightmare scenario in which the most restrictive jurisdiction with the will and ability to enforce its own domestic laws will set the world’s privacy standards (and, by implication, also the world’s speech and press standards). This practice also violates well-settled rules of international law that delimit enforcement authority based on the principle of territoriality. Although the Court of Justice of the European Union (CJEU), in Google LLC, recently rejected the issuance of a French global deindexing order to enforce the right to be forgotten (RTBF), its ruling rested on relatively narrow grounds (namely, that the General Data Protection Regulation (GDPR) does not, on its face, have extraterritorial effect). The CJEU’s decision clearly leaves open the possibility of global injunctions to enforce the RTBF if a regulation – unlike the GDPR – expressly provides for extraterritorial effect. Accordingly, the question of the global reach of remedies remains both pressing and important. If the CJEU ultimately were to follow the lead of the Supreme Court of Canada, and hold that global deindexing orders are consistent with international standards of comity and general conflict of laws principles, the need to create privacy safe harbours will become acute. Our current system, featuring vastly different local accommodations of privacy and speech/press rights, has managed to function only because domestic courts have generally refrained from insisting on making their own domestic rule the global privacy, or speech, standard. The emerging trend toward the issuance of global injunctions runs a nontrivial risk of subjecting data processors to inconsistent and conflicting legal standards. Content providers need to have the ability to control their susceptibility to judicial process through clear rules that lead to predictable outcomes. And remedies law needs to take into account the need for content providers and search engine providers to structure their operations in ways that permit them to cabin their legal exposure across jurisdictions. Failing to harmonize regulation and provide for safe harbours from local regulation will have a profound, and unacceptable, chilling effect on the global marketplace of ideas. In consequence, remedies law must take account not only of the need to safeguard privacy rights, but also of the need to respect domestic laws that safeguard expressive freedoms, including freedom of speech and the press, as well.