The Kolkata test of 2001 is one of the most famous results of an India-Australia test match. After being forced to follow-on, India came back strongly in the second innings, scoring a mammoth 657 runs and taking a lead of 383. Australia succumbed to 212, giving India the famous win.
The Chennai test of 1986 is another famous India-Australia test match. The match ended as a tie. As of June 2015, this is only the second instance of a tied test match in Cricket history. India needed 348 runs in the second innings and were dismissed for a total of 348 runs with two balls remaining and still requiring one run to win. The test is also famous for a splendid 210 scored by Dean Jones in extreme conditions.
Famous results of India-Australia matches with India winning the match are the Chennai test of 1998, Adelaide test of 2003, Perth test of 2008, 2011 World Cup Quarter final in Ahmadabad and the 1998 Coca-Cola Cup final in Sharjah.
Famous results of India-Australia matches with Australia winning the match are the Brisbane test of 1977, Adelaide test of 1992, third match of 1987 Reliance World Cup, twelfth match of the 1992 Benson & Hedges World Cup and the 2003 World Cup final in Johannesburg.