Laxman and 'Monkeygate': five classic Australia v India clashes
Some of the most competitive clashes have come since they began contesting the Border-Gavaskar Trophy -- named after the first two batsmen to pass 10,000 runs -- in the 1996-97 season.
AFP looks back at five memorable Tests:
Tendulkar conquers Warne
Sachin Tendulkar and spin king Shane Warne had many epic battles. But in 1998 at the Chidambaram Stadium, Chennai, Warne drew first blood by having the batting master caught for four in the slips, then he ran through the middle order to restrict India to 257 in their first innings. In reply, Australia made 328, helped by Ian Healy's 90.
This set the stage for Warne v Tendulkar round two, and it was the batsman who came out on top on a dusty, spin-friendly wicket. He produced one of his most dazzling innings, taking apart Warne and fellow spinner Gavin Robertson in a magnificent unbeaten 155 from 191 balls that changed the course of the match.
Laxman's epic stand
The second Test at Eden Gardens, Kolkata, in 2001 was all about one of India's greatest comebacks, and is regarded among the most exciting matches of all time. After Australia posted a big total of 445, with Matthew Hayden making 97 and Steve Waugh 110, their bowling attack led by Glenn McGrath skittled the home side for 171.
The follow-on was enforced with India in real danger of going 2-0 down in the series before VVS Laxman (281) and Rahul Dravid (180) knuckled down in a memorable and gritty 376-run stand for the fifth wicket as India made 657 for 7 before declaring.
Perhaps the most controversial and spiteful Test between the two nations, the 2008 Sydney encounter was dubbed the "Monkeygate" affair, marred by umpiring errors and accusations of racism.
Ricky Ponting's men won by 122 runs for a record-breaking 16th consecutive Test victory with just seven balls remaining in a breathless finish after part-time spinner Michael Clarke took three wickets in five deliveries.
But it is infamously remembered for Harbhajan Singh being charged with racial abuse and banned for three Tests for allegedly calling Andrew Symonds -- who has West Indian ancestry -- a "monkey" during the third day's play.
The row saw India threaten to pull out of the tour and on appeal the ban was lifted and the charge downgraded to abusive language, leaving relations between the teams tense.
Spinners rule in Bangalore
Australia took a 1-0 lead into the fiery Test in Bangalore in 2017 and when Nathan Lyon took 8-50 to bamboozle the Indian batsmen for 189, it looked like the tourists would go 2-0 up.
But in a bad-tempered few days, Ravi Jadeja picked up 6-63 to ensure the tourists led by just 87. A stylish 92 from Cheteshwar Pujara coupled with six wickets for Josh Hazlewood then saw India all out for 274 to set Australia 188 to win.
They crumbled for 112 with Ravi Ashwin becoming the fourth bowler in the match to claim six wickets -- the first time this had happened in Test history.
But the landmark was overshadowed by Virat Kohli accusing Australia of consulting their dressing room over DRS decisions from the field. Asked whether Australia cheated, a fired-up Kohli said "I didn't say that, you did."
Long drought ends in Adelaide
With Steve Smith and David Warner banned for ball-tampering, India capitalised to end a decade-long wait for a Test victory in Australia when they bowled out the home side for 291 to clinch the first game of their four-match series in 2018-19.
The hosts were set 323 to win, a score never before successfully achieved in a fourth innings run chase at the Adelaide Oval, with Australia falling a nail-biting 31 runs short despite a battling 60 from Shaun Marsh.
India put themselves in a position to win on the back of Cheteshwar Pujara's 123 in the first innings and 71 in the second during a match where wicketkeeper Rishabh Pant equalled the world record of most catches taken in a Test at 11.