The Supreme Court plunged into arguments Tuesday over the deportation of immigrants convicted of crimes, the first case in a term expected to more clearly define the Court’s direction under Chief Justice John Roberts.

Though the hallmark cases of the first full term for the current lineup of justices will come later when the Court hears disputes over abortion, race and the environment, the outcome of the first case on the schedule could affect thousands of immigrants who have run afoul of U.S. criminal law.