After the partition the majority of Sikh migrated from Pakistan to India mostly because of their prominent historical & religious places were in India as well as most of them migrated as sikh were in more population in India than Pakistan. The Punjab was a majority state to Sikhs but it was to merge with rest of Punjab to make a single province in India. The Sikhs were in more need of a separate province initially and the movement led by Akali Dal, a political party for Sikhs. Initially Indian government had rejected this and protest started to climb in mid 50s with Indian government done a major crack down of Sikh leaders and those who were the head of this movement.
However after the oppression did not get down instead arise to other parts of Punjab as well as 1965 war, India finally decided to give Sikhs a separate territory in Punjab while rest of Punjab was divided in to 2 states (Haryana and Himachal Pardesh presently). After this although Sikhs hag got their separate state but never got any rights and were just a piece of land with everything in Indian government hands. The Akali Dal started to demand more ruling rights from government which government denied. That made the basis of Khalistan.
Khalistan movement was recognized internationally when Jagjit Singh Chauhan went to US and started collecting funds for newly formed country (not recognized by anyone yet) and collected large sum of money from sikhs in US. They even introduced stamps and currency of Khalistan and held meetings in London to pressure for international community to recognize that.
As issue goes on the sikh youth turned in to militancy to acquire their rights. The oppression was pressed through operation blue start by indian army resulting in large massacre of sikhs as well as brutal destruction of their holy temples. This get more worse as sikhs were in more anger because they had lost large number of native sikhs and above all damage to one of their holiest places. This resulted in riots all over Punjab. Meanwhile as a retaliation indira gandhi was killed by his two sikh guards. After this another operation started which has killed thousand of sikhs.
The international community as well as neighboring countries criticizes how all this was handled and human rights violation by Indian government which are still going on. Khalistan tehreek is still alive and sikhs are demanding separate country. The main leaders of Khalistan movement are in exile currently living mostly in US & UK. They still demand their right for separate country.
While India talk about Balouchistan and Bugti political asylum, The India must not forget that Pakistan can also take similar steps which will result in Khalistan movement as strong as Kashmir dispute.