[11][12] The competition is a simulation of a fictional dispute between countries before the International Court of Justice (ICJ).

It is named after Philip Jessup, who once served on the ICJ, and is organised by the International Law Students Association (ILSA).

The Jessup moot involves arguing a hypothetical case on issues of international law as if before the ICJ, but with a smaller complement of judges (three instead of 15).

In each oral round, two competitors from a team will argue one side of the case for 45 minutes in total, including any time reserved for rebuttal or sur-rebuttal.

In other teams, only two or three speakers will present oral argument, with at least one person arguing both Applicant and Respondent sides.

In addition, most teams include at least one advisor or coach, usually drawn from the respective universities' international law faculty and/or past Jessup competitors.

For instance, historically, the United States, which has more than a hundred law schools taking part each year, is represented by up to 12 teams following the conclusion of its six regional rounds, while smaller countries that have only a small number of law schools can only send one team.

In recent years, around 700 schools worldwide participate in the competition, with the top 140 or so qualifying for the international rounds in Washington, D.C.