During the third ODI match between India and Australia on January 19, 2020, India skipper Virat Kohli set the record for the fastest batsman to score 5,000 runs as a captain of an ODI team. Virat achieved this feat in 82 innings. Kohli broke the previous record which was set by former India captain MS Dhoni (127 innings).

During the third ODI match between India and Australia on January 19, 2020, Virat Kohli also became the fifth batsman to score his 100th 50-plus score in ODIs.

During the third ODI between India and Australia on December 2, 2020, Virat Kohli scored his 12,000th run in ODI cricket. Kohli went on to break Sachin Tendulkar's record to become the fastest batsman to 12,000 runs in ODIs.

During the first ODI match between India and Australia on November 27, 2020, all-rounder Hardik Pandya set the record for the fastest Indian batsman to score 1,000 runs in ODIs, in terms of balls faced (857).

During the third T20I between India and New Zealand on January 29, 2020, Rohit Sharma scored his 10,000th run across all three formats of international cricket as an opening batsman.

During the third ODI match between India and Australia on January 19, 2020, India's star opening batsman Rohit Sharma scored his 9,000th run in ODIs and is the seventh-highest in terms of Indian cricketers to do so.

During the first Test match against Australia on 17 December 2020, Team India was dismissed for a total of 36 runs in 21.2 overs. This was India's record lowest ever Test total. This was the first instance in a Test match wherein all the eleven batsmen, along with extras, did not cross single-figures in an innings. Earlier, on February 29, 2020, India also scored the second-lowest total of the year 2020 (124) vs New Zealand in 46 overs.

During the second ODI  match between India and Australia on January 17, 2020, spinner Kuldeep Yadav entered the record books when he became the fastest spinner for Team India to take 100 ODI wickets in the least amount of innings (58).

During the first T20I between India and Australia on  December 4, 2020, spinner Yuzvendra Chahal became the first concussion substitute to ever be named the Man of the Match in the history of international cricket.

During the fifth T20I between India and New Zealand on February 5, 2020, Shivam Dube bowled the second-most expensive over in a T20I match after he conceded 34 runs. Tim Seifert and Ross Taylor scored 17 runs each off his over.

During the IPL 2020 match between Chennai Super Kings and Rajasthan Royals, CSK skipper MS Dhoni became the first cricketer to ever play 200 matches in IPL.

During the IPL 2020 match between Delhi Capitals and Royal Challengers Bangalore, RCB skipper Virat Kohli set the record as the first Indian cricketer to score 9,000 T20 runs.

During the IPL 2020 match between Kings XI Punjab and Royal Challengers Bangalore, KXIP skipper and opener KL Rahul set a record for the highest individual score by an Indian batsman in the IPL as well as the highest individual score by an IPL captain in the IPL (132). KL Rahul also set a record to become the first Indian player to score over 500 runs in three back-to-back IPL seasons.

During the IPL 2020 match between Delhi Capitals and Kings XI Punjab, DC opener Shikhar Dhawan became the 5th overall and the 4th Indian cricketer to reach the 5000-run mark in IPL. Dhawan  also went on to set the record as the first-ever cricketer to score two consecutive centuries in IPL. He was also the 5th cricketer to score multiple hundreds in a single IPL season.

During the IPL 2020 match between Kolkata Knight Riders and Royal Challengers Bangalore, Mohammed Siraj became the first bowler to bowl two maiden overs in an IPL match.