The remains were taken from Ainu grave sites primarily in Japan's northern island of Hokkaido, but also from the Sakhalin and Kurile Islands (now part of Russia) between 1873 and 2011 for anthropological research, especially on the skulls.
At the centre of the controversy is Hokkaido University, which is holding the majority of the remains - those of 1027 individuals - and a lawsuit has been filed against the university by a group of Ainu from the Kineusu kotan seeking to have the bones returned.
The Ainu are the indigenous people of Japan's northern island of Hokkaido and also the Kurile and Sakhalin Islands of Russia's far east.
They are a distinct ethnic group to the Yamato Japanese and have lighter skin, more body hair and rounder eyes, giving them a more European appearance, although recent DNA research suggests they are not actually Caucasian, but of "proto-mongoloid" genetic stock.
The Ainu were an ancient hunter/gatherer society with their own language, culture and a religion based on natural phenomenon - although it is believed there are now almost no native Ainu speakers left alive.
Until the 18th century, the Ainu lived in relative isolation on Hokkaido and maintained a society independent of the Japanese although extensive interactions through trade, and some conflict, did occur.
Then after the Meiji Restoration in 1868, Hokkaido was formally annexed by the Japanese and in 1899 the Hokkaido Former Aborigines Protection Act was passed.
This law marked the beginning of the end of traditional Ainu culture and society, and led to forced assimilation of the Ainu into mainstream Japanese life and the loss of customary hunting and fishing rights.
It wasn't until 2008 that the Japanese diet finally passed a resolution formally recognising the Ainu as the indigenous people of Japan.
The current Ainu population of Japan is estimated to be somewhere between 25,000 and 200,000.