Main article: Arbitration award
Although arbitration awards are characteristically an award of damages against a party, in many jurisdictions tribunals have a range of remedies that can form a part of the award. These may include:
- payment of a sum of money (conventional damages)
- The making of a "declaration" as to any matter to be determined in the proceedings
- In some[which?] jurisdictions, the tribunal may have the same power as a court to:
- Order a party to do or refrain from doing something ("injunctive relief")
- To order specific performance of a contract
- To order the rectification, setting aside or cancellation of a deed or other document.
- In other jurisdictions, however, unless the parties have expressly granted the arbitrators the right to decide such matters, the tribunal's powers may be limited to deciding whether a party is entitled to damages. It may not have the legal authority to order injunctive relief, issue a declaration, or rectify a contract, such powers being reserved to the exclusive jurisdiction of the courts.
Generally speaking, by their nature, arbitration proceedings tend not to be subject to appeal, in the ordinary sense of the word. However, in most countries, the court maintains a supervisory role to set aside awards in extreme cases, such as fraud or in the case of some serious legal irregularity on the part of the tribunal. Only domestic arbitral awards are subject to set aside procedure.
In American arbitration law there exists a small but significant body of case law which deals with the power of the courts to intervene where the decision of an arbitrator is in fundamental disaccord with the applicable principles of law or the contract. However, this body of case law has been called into question by recent decisions of the Supreme Court.
Unfortunately there is little agreement amongst the different American judgments and textbooks as to whether such a separate doctrine exists at all, or the circumstances in which it would apply. There does not appear to be any recorded judicial decision in which it has been applied. However, conceptually, to the extent it exists, the doctrine would be an important derogation from the general principle that awards are not subject to review by the courts.
The overall costs of arbitration can be estimated on the websites of international arbitration institutions, such as that of the ICC, the website of the SIAC  and the website of the International Arbitration Attorney Network. The overall cost of administrative and arbitrator fees is, on average, less than 20% of the total cost of international arbitration.
In many legal systems - both common law and civil law - it is normal practice for the courts to award legal costs against a losing party, with the winner becoming entitled to recover an approximation of what it spent in pursuing its claim (or in defense of a claim). The United States is a notable exception to this rule, as except for certain extreme cases, a prevailing party in a US legal proceeding does not become entitled to recoup its legal fees from the losing party.
Like the courts, arbitral tribunals generally have the same power to award costs in relation to the determination of the dispute. In international arbitration as well as domestic arbitrations governed by the laws of countries in which courts may award costs against a losing party, the arbitral tribunal will also determine the portion of the arbitrators' fees that the losing party is required to bear.