Here is a look at how the affirmative action case twice made its way to the court:

Q: What is the case about?

A: In 2008, the University of Texas at Austin denied admission to Abigail Fisher, a white woman. Three-quarters of applicants from Texas are admitted under a program that guarantees admission to roughly the top 10 percent of students in every high school in the state. The remaining Texas students and those from elsewhere are considered under standards that take account of academic achievement and other factors, including race and ethnicity. Fisher sued over that second part of the admissions plan, saying that it violated the Constitution's equal protection clause.

Q: What does Fisher want?

A: As a legal matter, she wants to do away with racial preferences in admissions decisions at the university. But to have standing to sue, she must also show that she has a personal stake in the question. Given that she has graduated, from Louisiana State University in 2012, that may not be easy.

Q: What happened last time?

A: The justices first heard arguments in the case in October 2012. After unusually fraught deliberations, a fiery draft dissent from Justice Sonia Sotomayor helped pave the way for a short, wan compromise decision in June 2013. By a 7-1 vote (Justice Elena Kagan has recused herself because she worked on the case as U.S. Solicitor General), the court returned the case to a federal appeals court. Last year, the appeals court upheld the program for a second time. In June, the Supreme Court agreed to take another look at the case.

Q: Who will hear the case?

A: Without Kagan, there will be only eight justices on the bench. A 4-4 tie would automatically uphold the appeals court's decision.

Q: What has happened since the last major affirmative action case?

A: In 2003, by a 5-4 vote, the court upheld the admissions plan at the University of Michigan's law school. Writing for the majority in the case, Justice Sandra Day O'Connor said the school could not use quotas but could consider race as one factor of many in order to construct a diverse student body. Saying that the Constitution ordinarily forbids the government from sorting people by race, she suggested that this exception would last for 25 years.

We are about halfway there. But O'Connor retired in 2006 and was replaced by Justice Samuel Alito, who has voted with the court's more conservative justices in decisions involving race.

As usual, the crucial vote belongs to the member of the court at its ideological center, Justice Anthony Kennedy. His views on when the government can take account of race are not always easy to pin down, but he has never voted to uphold an affirmative action program.

Q: How significant will the court's ruling be?

A: It is possible that the court will reaffirm the 2003 decision, but that is not the most likely outcome. The court may strike down only Texas' program. Or it may say that the Constitution forbids the use of race in admissions decisions at public colleges and universities nationwide. That would almost certainly also mean that affirmative action would be banned at most private ones as well.

New York Times