The evolution of affirmative action as case law is as follows: 

Regents of University of California v. Bakke (1978):
Allan Bakke, a Caucasian student, sued the Medical School of the University of California at Davis based on the Equal Protection Clause and Title VI of the Civil Rights Act of 1964. The university had a special admission program under which 16 of 100 positions in the class were reserved for disadvantaged minority students. Bakke's admission was refused twice, although his admission results were significantly higher than those of other applicants admitted in the second selection procedure. The court upheld the general right of schools to consider race as a factor in their admission process. The basic principle of the Bakke decision was that, while schools cannot outright exclude anyone based on race, they could use race as a “plus” factor that could be considered in an individual’s admission along with other salient factors. 

Grutter v. Bollinger (2003):
Twenty-five years later, the Supreme Court again upheld the general right of schools to consider race in their admissions policies. The case will be discussed in detail here.

Parents v. Seattle (2007) and Meredith v. Jefferson (2007):
The court decided by a 5-4 margin that public school systems can’t seek to maintain integration through measures that take into account a student’s race, on constitutional grounds. 

Fisher v. University of Texas (2013):

In the Fisher case, the court ruled that the race-conscious admission program of the University of Texas was admissible. The case will be discussed here.

These Supreme Court cases have given rise to legislation on affirmative action by both the federal and state governments. Naturally, the Supreme Court’s position on this subject has changed over time.