The Supreme Court most recently addressed affirmative action admissions policies in a 2016 case, Fisher v University of Texas, voting 4 to 3 to uphold a modest race-conscious program at the University of Texas at Austin, which guaranteed admission to the top students in each Texas high school and often produced significant racial and ethnic diversity. The remaining students accepted to UT are considered under standards that take into account academic achievement and other factors, including race and ethnicity.
This question is not new. The Supreme Court, going as far back as a 1978 case Regents of the University of California v. Bakke, has ruled that the educational benefits that flow from having a diverse student body can justify using race as one factor among many in a “holistic” evaluation. However, the court essentially rejected blunt racial quotas or race-based point systems, as it did in rulings in two separate cases in 2003 against the University of Michigan (Gratz v. Bollinger) and the University of Michigan Law School (Grutter v. Bollinger).
What the rulings permit in actual practice by universities is often murky. And there are several pending lawsuits challenging such practices at other universities, including Harvard and the University of North Carolina.