World number one and second seed Nadal tackles Australian wildcard Nick Kyrgios, the world number 144 who has enjoyed a dream debut at the All England Club.
The 19-year-old is bidding to become the first player ranked outside the top 100 to defeat a world number one since Andrei Olhovskiy, ranked at 193, defeated Jim Courier in the third round at Wimbledon in 1992.
“I never thought that I would be seeing Nadal in my fourth round Wimbledon in my 19th year. I thought it would take years and years of work to finally have an opportunity like that,” said Kyrgios as he takes aim at the 14-time major winner.
Seven-time champion Federer takes on fellow 32-year-old Tommy Robredo, the man who ended a 10-match losing streak to the great Swiss at the US Open last year.
Robredo, the 23rd seed, is bidding to reach his first Wimbledon quarterfinal and complete a set of Grand Slam quarterfinal appearances.
He is also chasing his 100th Grand Slam match-win in his 50th Grand Slam tournament.
The other last-16 ties on Tuesday see fifth seeded Australian Open champion Stan Wawrinka face Feliciano Lopez of Spain while Canadian eighth seed Milos Raonic takes on Japan’s 10th seed, Kei Nishikori.
All four matches should have been played on Monday but were put back because of rain hitting the Saturday schedules which left three third round matches still to be played.
The chaos had Wawrinka fuming as he faces the prospect of playing five matches in seven days to win the title.