Arbitration is a way to solve a conflict, but it is not the only way to solve conflicts; there is not really a confrontation between Arbitral justice and ordinary justice; conciliation and arbitration are not methods exclusively directed to clear or banned ordinary justice, but just two of several ways to manage conflict resolution. In Colombia, arbitration is a true process; the arbitral award (laudo) is a true judgment; Arbitrators are true judges who serve justice with jurisdictional character, emanated directly form the sovereignty of the State. The so called “amigable composición” is not a jurisdictional process, it is other way to solve conflicts, not as a “jurisdictional” matter, but by a way of contractual agreement between the parties in dispute; their decision are not similar to a judgment sentence but to a convention, and the “amigables componedores” are not truly judges but just empowered by both parties to reach a solution of their differences; the amigable composición has neither rules of proceeding nor resources, not even applicable legislation like the Arbitration proceedings. “Due process” requires the fulfillment of “procedural forms” as states art., 29 of the Colombian Political Constitution by the expression “observance of the fullness of the proper forms of each judgment”. Those who plead for “an informal” Arbitration forgot that Arbitration in Colombia is a true “process” that must follow “the proper forms of each judgment”; thus, they should try the proceedings of an “amigable composición”. In a national arbitration, Arbitrators are truly Colombia judges that exerts jurisdiction by virtue of the sovereignty of the State; in international Arbitration, the Arbitrators are not judges of any State; therefore, they do not exert its functions by virtue of any sovereignty, nor are forced by any law. For the later reasons, the power of the judgment emanates by the designation that the parts have done to them; they can decide what law should apply the case and the ruling, because their arbitral award (laudo) is generally rendered aequo et bono. Whenever the arbitral award (laudo) needs to be executed in some other State, generally must have to pass through an exequatur proceeding, in order to have a national Court of that State, to examines if the award fulfills the minimum requirements needed to have that decision as a national award.