The 2018-19 maiden Test series win in Australia was then arguably India’s biggest victory in the last few decades.

The tourists took full advantage of Australia’s weakness. They were without their former skipper Steven Smith and big-hitting opener David Warner (both banned for ball-tampering in South Africa). The first Test at Adelaide was a thriller as India registered their first win in Australia in over 10 years. Chasing 323, Australia fell short by 31, thanks to three wickets each by pacers Jasprit Bumrah, Mohd Shami and offie R Ashwin. The Aussies, however, made a comeback in the second Test at Perth to level the series 1-1.

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A century by in-form batsman Cheteshwar Pujara helped India post 443-7 declared in the first innings of the third Test. In reply, India’s pace bowling sensation Bumrah grabbed 6-33—the second-best figures by an Indian fast bowler in Australia—to rattle the hosts for just 151 and take a mammoth 292-run lead. Kohli did not enforce the follow-on as India declared their second innings for 106-8 to set Australia a 399-run target. The hosts managed just 261 in the second essay as India went on to win the Test by 137 runs to take a 2-1 lead in the four-match series and retain the Border-Gavaskar Trophy. The victory also saw Kohli equalling Sourav Ganguly’s record of most wins (11) by an Indian Test captain abroad.

The rain-hit fourth Test at Sydney ended in a draw as India scripted history to win their first-ever series in Australia, 71 years after they first toured Down Under.

2-1 v Sri Lanka in 2015-16

This was India’s first full-fledged Test series under the leadership of Kohli. The opening Test of the three-match series didn’t go India’s way as the visitors failed to achieve the 176-run target on Day Four (August 15, 2015) to give the country an Independence Day gift. The hosts restricted India for just 112, as the visitors suffered a shock 63-run defeat. This was India’s lowest-ever total against Sri Lanka.
But Kohli’s men made a strong comeback in the second match to spoil Sri Lankan wicketkeeper-batsman Kumar Sangakkara’s farewell. India had a near-perfect game, scoring 393 and 325-8d in the first and second innings respectively as the tourists set Sri Lanka a target of 413. Despite a rain scare, India managed to beat Sri Lanka by 278 runs on the final afternoon for their first Test win in a year.

India scripted history by beating the hosts by 117 runs in the third Test for their first Test series win in Sri Lanka since 1993. The series also witnessed Indian bowlers claiming all 60 wickets of the opposition in a three-Test series for the first time since the 1988-89 home series against New Zealand.

3-0 v Sri Lanka in 2017-18

A lot was expected from Team India on the back of their last series win in Sri Lanka, and the visitors didn’t disappoint. India lost just 32 wickets in the three-match series as compared to Sri Lanka’s 60. The hosts didn’t come close to victory even in a single Test.

Kohli’s men demolished Sri Lanka by 304 runs in the first Test, an innings and 53 runs in the second match and by an innings and 171 runs in the third as India went on to create history with the first whitewash in an away series of three or more Tests. It also witnessed India winning three matches in an away Test series for the first time since they beat New Zealand 3–1 in 1967–68.

4-0 v England in 2016-17

India hosted England in a five-match Test series for the first time since 1984-85, also India’s first on home soil since the 1986-87 series against Pakistan.

England started the tour on a positive note, scoring a mammoth 537 in the first innings of the opening Test at Rajkot. With India needing 310 to win on Day Five, the visitors came close to achieving victory by reducing the hosts to 132-6. But India fought back to draw the first Test.

There was no looking back for India thereafter as they went on to thrash England in the remaining four matches with the fifth Test at Chennai witnessing several records being broken. The victory also took the hosts’ unbeaten streak to 18 matches, a then-record set by India. England became the first team to lose a Test by an innings after scoring 477 in the first essay as the hosts, in reply, posted a mammoth 759-7 declared, their highest-ever total in Test cricket. Karun Nair’s first innings triple ton (303') was the icing on the cake as he became only the second Indian to score a triple Test century. India went on to win the match by an innings and 75 runs to clinch the five-match series 4-0.

3-0 v New Zealand in 2016-17

The first Test at Kanpur was India's 500th Test, and the team celebrated the occasion by registering a 197-run win over New Zealand. Despite almost 1,200 runs scored by both teams in the first Test, the match did not witness a single centurion, a rarity in Test cricket. Ashwin’s 6-132 in the second innings and 10-wicket match haul helped India complete a historic win in the landmark Test.

The second match at Kolkata witnessed another landmark—India's 250th Test at home. Kohli’s men repeated their first Test show as the clinical performance helped the hosts grab the series with a 178-run victory. The win also ensured India’s rise to the top of the ICC Test rankings.

The third Test was a cakewalk for India after Kohli (211) and Ajinkya Rahane (188) put on a massive 365-run partnership for the fourth wicket as the hosts declared their innings at 557-5. The visitors thereafter never seemed to be in the game as India hammered New Zealand by 321 runs to wrap up the series 3-0, their first clean sweep against the Kiwis in Test series involving three or more games.