Harvard, Stanford, and MIT are the top 3 universities in the world, according to the 2015 Academic Ranking of World Universities list compiled by researchers at the Center for World-Class Universities of Shanghai Jiao Tong University and published each year. An August 16 press release summarizes the list:

Starting from 2003, ARWU has been presenting the world Top 500 universities annually based on transparent methodology and third-party data. It has been recognized as the precursor of global university rankings and the most trustworthy one.

While the website explains its methodology:

Universities are ranked by several indicators of academic or research performance, including alumni and staff winning Nobel Prizes and Fields Medals, highly cited researchers, papers published in Nature and Science, papers indexed in major citation indices, and the per capita academic performance of an institution. For each indicator, the highest scoring institution is assigned a score of 100, and other institutions are calculated as a percentage of the top score. The distribution of data for each indicator is examined for any significant distorting effect; standard statistical techniques are used to adjust the indicator if necessary. Scores for each indicator are weighted as shown below to arrive at a final overall score for an institution. The highest scoring institution is assigned a score of 100, and other institutions are calculated as a percentage of the top score. An institution’s rank reflects the number of institutions that sit above it.

Harvard University has never dropped below #1 in the 13 years the list has been published, while Stanford has never ranked lower than #3. The highest ranking Asian university in 2015 is The University of Tokyo at #21, while no Korean universities place in the top 100.