The world No. 1 takes on Spain's Pablo Carreno Busta, while Medvedev plays Australia's Alexei Popyrin.
The 23-Grand Slam winner suffered a shock third round loss against 6-4, 6-7 (2-7), 7-5 to China's Wang Qiang.
Williams faces China's Wang Qiang, while Federer takes on Australia's John Millman and Coco Gauff plays Naomi Osaka.
Williams faces Slovenia's Tamara Zidansek, while Federer takes on Serbia's Filip Krajinovic and Djokovic plays Japan's wild card Tatsuma Ito.
The first Grand Slam of the season begins in Melbourne on Monday, with some of the tournament favorites all in action.
The 108th edition of the Australian Open gets underway in Melbourne on Monday, with the women's and men's final scheduled for the first weekend of February.
Novak Djokovic and Serena Williams are the bookmakers' favorite to add an eighth Australian Open title to their collections this year.
The first Grand Slam tournament of 2020 gets underway on January 20 in Melbourne with Novak Djokovic and Naomi Osaka looking to defend their titles.
Roger Federer, Novak Djokovic, Rafael Nadal and Serena Williams are among the players in action in the fundraiser for the victims of the bushfires.
The former world tennis number one won her first prize in three years in Melbourne and has said she will donate the prize money to help fund bushfire relief efforts.
The 34-year-old won the World Cup in July and was named player of the tournament, before adding the FIFA World Player of the Year in September and the Ballon d'Or last month.
Serena Williams looks for a record-equalling 24th Grand Slam title, while Bianca Andreescu could become the first Canadian to win a major.
Serena Williams looks for a second consecutive U.S. Open Final when she plays No. 5 seed Elina Svitolina on Thursday night.
The Spaniard is odds-on favorite to win a 19th Grand Slam title after Novak Djokovic and Roger Federer were both knocked out.
Federer chases a first semifinal at Flushing Meadows since 2015, while Williams looks to take another step towards a 24th Grand Slam title.
Federer takes on Britain's Dan Evans, while Djokovic faces American qualifier Denis Kudla on Friday evening.
Coco Gauff plays Hungary's Timea Babos, while Rafael Nadal takes on Australia's Thanasi Kokkinakis on Thursday.
The world No. 1 and the world No. 3 are both in action on Wednesday, as are the Williams sisters.
Rafael Nadal and Coco Gauff are both in action on Tuesday as the first round of the U.S. Open is completed.
At the Wimbledon final on Saturday, Serena Williams was denied a record-equalling 24th grand slam title by Romanian Simona Halep, who secured her first Wimbledon crown on Centre Court.
Serena Williams chases a record-equaling 24th Grand Slam title when she faces Romania's Simona Halep in the final on Saturday.
"Oh to have the confidence of a mediocre white man," tweeted one commenter on a new YouGov poll about Serena Williams.
Serena Williams has a 9-1 career record against Simona Halep and the pressure will be firmly on her shoulders Saturday.
The 23-time Grand Slam winner faces Barbora Strycova of the Czech Republic in her 12th semifinal at Wimbledon.
Serena Williams takes on Barbora Strycova of the Czech Republic, while former world number one Simona Halep plays number eight seed Elina Svitolina.
After the match, Williams questioned whether she should have stayed silent but after speaking with Osaka, she realized she needed to continue fighting against injustice.
The 23-time Grand Slam winner takes on Alison Riske in an all-American quarterfinal on Centre Court on Tuesday.
Tennis's new teenage sensation is in action against former world number one Simona Halep, while Williams plays number 30 seed Carla Suarez Navarro.
The 15-year-old Gauff needed all 2 hours, 47 minutes to hold off Slovenia's Polona Hercog Friday afternoon in London.
Federer plays Britain's Jay Clarke in the second round, while Nadal takes on Nick Kyrgios in a potentially tricky encounter.