This thesis concerns the issue of injunctive relief and specific performance in arbitration. The availability of such relief varies significantly between different jurisdictions and the issue is further complicated when parties opt out of litigation in favor of arbitration, not the least in terms of enforcement. In light of this, the thesis aims to determine the consequences for parties opting for arbitration instead of litigation with regard to the availability and enforceability of specific performance and injunctive relief. This overall research question has been answered under the laws of Sweden and the United States of America. First, this thesis has concluded that there are considerable differences between the jurisdictions in the availability of specific performance and injunctive relief in litigation. In Sweden, remedies are issues of substantive law and for many kinds of contracts, the primary remedy for breach. Consequently, courts do not differentiate claims for specific performance or injunctive relief, and routinely grant such claims in no different way than granting monetary relief. Conversely, in the United States, remedies are viewed as procedural issues, not substantive. There, specific performance and injunctive relief are discretionary matters of equity and not rights at law. Hence, the availability of specific performance and injunctive relief is limited as compared to damages. Further, this thesis has concluded that the categorization of reliefs and remedies as substantive and procedural, respectively, is mirrored also in arbitration. While in Sweden, the choice of arbitration as proper contract forum does not affect the availability of the reliefs now in question, it does so in the United States. There, courts have held that the division of remedies into legal and equitable is not applicable in arbitration. Thus, parties have the freedom to by contract control which reliefs an arbitrator may grant. In absence of such agreements, courts have presumed arbitrators to have been given a broad grant of authority, allowing otherwise unavailable reliefs.Third, this thesis has concluded that, inter alia, because of the inherent contempt powers of courts in the United States, the means of enforcing arbitral awards providing specific performance and injunctive relief are more extensive in the United States than in Sweden, where comparable powers do not exist. Further, parties may by means of contract, grant arbitrators the authority to supervise such reliefs and enforce previously granted specific performance and injunctions by contractual fines and sanctions. Again, in absence of explicit contract language such authority is presumed in the United States, but not in Sweden. Overall, the choice of arbitration has consequences in both jurisdictions. In the United States, mostly for the availability of the reliefs in question and in Sweden, mostly for the enforcement.