This chapter explores the potential role of national and international courts and tribunals in relation to claims for environmental damage to areas beyond national jurisdiction (ABNJ). Access to remedies includes facilitating access to international and national courts to initiate claims for environmental harm, but also requires consideration of the associated rules that may constrain the ability of the court or tribunal in question to provide relief, such as jurisdiction, rules on the choice of law and the recognition and enforcement of judgments rendered in such cases. The chapter begins with a discussion of the general rules and principles concerning access to remedies under the rules of state responsibility and domestic civil liability, respectively, before turning to the specific rules in ABNJ. It also addresses the substantial additional challenges that each of these sets of rules pose to realizing the goals of liability regimes, including the need to prevent environmental harm and restore the environment, to provide for effective deterrence of risky behaviour, to ensure a level playing field and to ensure adequate and prompt compensation.