It's interesting to learn that the U.S. Department of Education is looking into allegations that Harvard and Princeton are discriminating against Asian-American applicants, but it's worth noting that we know perfectly well that this discrimination happens. The only real issue is whether or not they're breaking the law.
I'll speak directly to Harvard, since I reported on admissions practices when I was a student there, but it in no important way differs from other Ivy League schools in this regard. For starters, Harvard recruits athletes who are disproportionately white (it's not just football and basketball—there are fencing and golf teams). Harvard also gives a bonus to the children of alumni, another disproportionately non-Asian group. But then on top of that Harvard seeks to ensure the presence of a diverse class by giving bonuses to members of underrepresented racial minorities and underrepresented geographical areas. The much-discussed racial diversity criteria hurt Asian applicants and benefit black and Latino applicants, while the never-discussed geographical diversity criteria hurt Asian applicants and benefit whites. Conservatives have entrenched into law the idea that policies with a "disproportionate impact" on racial minorities don't constitute an illegal form of discrimination, which may be the wise approach, in which case it may be that Ivy League schools aren't doing anything illegal to Asian applicants. But it's clear enough that the structure of their admissions policies has the effect of disadvantaging Asian applicants. However these cases shake out, it seems very likely to me that 50 years from now we'll look back on this period in American higher education as very similar to the old informal quota system that used to cap the number of Jewish students at the same schools. In both cases, you don't need to posit any bias or ethnic animus to explain the policies. The mission of Harvard and Princeton are to serve as inculcators of a certain kind of American social elite and that drives all these goofy admissions policies.
CORRECTION, February 15: The initial draft said that racial and geographical diversity preferences hurt Asian applicants "at the expense" of blacks, white, and Latino applicants rather than to benefit them.