[5] In July 2019, he was suspended by Board of Control for Cricket in India for a doping violation, the suspension lasting until November of the same year.

[13][14][15] In February 2023, after an affray in a nightclub, YouTuber Sapna Gill and her male friends followed Shaw's vehicle, vandalised it, and manhandled him.

[17] In November 2013, he had set the highest score by any batsman in any organised form of cricket since 1901 when he hit 546 in a Harris Shield elite division match.

[18] Shaw captained the Rizvi Springfield team to two Harris Shield tournament titles in 2012 and 2013, a prestigious trophy in Mumbai's youth cricket.

[20] In April 2012, Shaw was invited to England to play for Cheadle Hulme School in Manchester and scored 1,446 runs during a two-month stay, including a century on debut,[21] and averaged 84.

During his time in Manchester, Shaw made several appearances for local side High Lane Cricket club.

He opened the batting and scored 68 in under 10 overs, before a change of pace in English conditions led to his dismissal, caught off the bowling of Professor Paul Wordsworth.

[24] In November 2017, batting for Mumbai in the 2017–18 Ranji Trophy, he scored his second consecutive century, and his fourth in five first-class matches since his debut.

[38][39] On 23 April 2018, at the age of 18 and 165 days, Shaw became the youngest player to open batting in Indian Premier League history while playing for Delhi Daredevils in their match against Kings XI Punjab.

[44] In November 2013, Shaw established a new record of 546 runs from 330 balls playing for Rizvi Springfield in a Harris Shield match.

[46][47] Previously, the highest score recorded by an Indian in any form of registered competitive cricket was 515 by Dadabhoy Havewala in 1933.

[49] The innings attracted significant media attention, particularly as it came only four days after the official retirement from international cricket of Sachin Tendulkar, who had scored 326 in the same tournament in 1988.

[55] In January 2020, Shaw was named in India's One Day International (ODI) squad for their series against New Zealand.

[58] In December 2020, Shaw performed poorly in the first Test against Australia, scoring 0 and 4, following which his batting technique was questioned and was dropped for the next match.