The No. 2-ranked Medvedev had a 6-4, 6-4, 6-2 win over Botic Van de Zandschulp in the third round, two days after a challenging second-round win over Nick Kyrgios.
The 14th-seeded Halep advanced with a 6-2, 6-1 victory Saturday over Danka Kovinic, a player who is ranked 98th and eliminated U.S. Open champion Emma Raducanu in the previous round.
The sixth-seeded Nadal, aiming for a men's record 21st Grand Slam singles title, didn't get it all his own way in an afternoon match on Rod Laver Arena.
Bopanna and his French partner Edouard Roger-Vasselin lost in three sets to wild card pair of Chirstopher Rungkat and Treat Huey.
Barty extended her streak of service holds to 48 games and moved into the third round at Melbourne Park for the sixth consecutive year by beating 142nd-ranked qualifier Lucia Bronzetti 6-1, 6-1 in under an hour Tuesday in Rod Laver Arena.
The former No 1-ranked Murray, playing thanks to a wild-card invitation as he continues his career comeback from hip operations and thoughts of retirement, beat 21st-seeded Nikoloz Basilashvili 6-1 3-6 6-4 6-7(5) 6-4 on Tuesday to reach the second round at Melbourne Park.
"International Tennis Federation (ITF) protocols at major events meant an unvaccinated player would be entitled to enter France and participate in Roland Garros, which begins in May, said Roxane Maracineanu.
Djokovic won his court appeal this week against a border official's decision to cancel his visa. He won over procedural errors related to Australia's confusing COVID-19 vaccination regulations.
The Australian government has canceled his visa twice and Djokovic's lawyers have appealed twice.
Djokovic was not seen on the online feed available to the public for the 15-minute procedural hearing, which began just two days before he is scheduled to play his first match of 2022 at Melbourne Park.
This decision followed orders by the Federal Circuit and Family Court on 10 January 2022, quashing a prior cancellation decision on procedural fairness grounds.
Immigration Minister Alex Hawke said Friday he used his ministerial discretion to revoke the 34-year-old Serb's visa on public interest grounds three days before the Australian Open is to begin.
The latest holdup has to do with an anticipated decision from the country's immigration minister on Djokovic's back-and-forth status.
Despite the cloud hanging over Djokovic's ability to compete, Australian Open organizers included the top seed in the draw.
A statement was posted on Djokovic’s social media accounts Wednesday while the men’s tennis No. 1 was in Rod Laver Arena holding a practice session against Tristan Schoolkate, a 20-year-old Australian.
"The whole situation regarding Novak Djokovic is closed by the verdict of the Australian court," Srdjan Djokovic told Bosnian Serb TV station RTRS.
After a confusing day-long hearing involving dense legal arguments, Djokovic was ordered to be released from immigration detention on procedural grounds.
In a clash between the tournament's two previous winners, No 1 seed Barty beat No 5 seed Swiatek 6-2, 6-4 in 1 hour and 27 minutes to keep alive her hopes of regaining the title she claimed in 2020.
The pair of Sania and Nadiia beat their opponents 6-0, 1-6, 10-5 in a quarterfinal clash that lasted for 55 minutes. The Indo-Ukranian duo will now face Australia combination of Ashleigh Barty and Storm Sanders in the last-four round of the event.
The top-ranked Djokovic announced on social media Tuesday that he had “exemption permission” and landed in Australia late Wednesday after receiving a medical exemption from the Victoria state government that would shield him from the strict vaccination regulations in place for this year's first major tennis tournament.
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