Robredo has reached the French Open quarterfinals four times before, but never gone farther.
France are also safely through to the quarterfinals with a 3-0 win over Israel in Rouen.
He will play home hope and 16th seed Milos Raonic for a place in the quarterfinals.
Taylor scored the fall over Appalachian State's Zachary Strickland to earn his spot in the quarterfinals.
At the French Open, Djokovic saved four match points in the quarterfinals against Tsonga.
Serena Williams, who lost in the quarterfinals, will take the number-two rank in the world.
British boxer Savannah Marshall was the favorite to win gold but was defeated in the quarterfinals.
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It was the first time this year she has got past the quarterfinals of a tournament.
In Thursday's quarterfinals, fifth seed Robin Soderling of Sweden takes on No. 13 Mikhail Youzhny of Russia.
Poland's Agnieszka Radwanska eased into the quarterfinals when she beat Hungary's Greta Arn of Hungary 6-3, 6-4.
She knocked out top seed Maria Sharapova in Friday's quarterfinals, her first-ever win over a top-10 player.
Maria Sharapova booked her place in the quarterfinals with a comfortable 6-2 7-5 win over Germany's Sabine Lisicki.
Azarenka, who went 26-0 before losing at the quarterfinals in Miami last year, is now 14-0 in 2013.
Ms. May-Treanor and Ms. Walsh Jennings won their third gold medal, while the men lost in the quarterfinals.
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After three exciting quarterfinals, the fourth was always likely to be the scrappiest -- and so it proved.
But Al Anabi, or The Maroon as the team is know, managed to reach the quarterfinals in the end.
Second seed Nadal reached the quarterfinals for a sixth successive year after beating 13th-seeded American John Isner 7-5 6-4.
The Serbian opens his account on Tuesday against Sergiy Stakhovsky of Ukraine, and could meet Robredo in the quarterfinals.
Earlier Zheng's compatriot Li Na followed her into the quarterfinals after stunning fourth seed Caroline Wozniacki in straight sets.
Should he win, the U.S. will play Serbia in the quarterfinals in April.
Meanwhile, defending champion Serena Williams cruised into the quarterfinals with a crushing 6-2 6-0 win over Slovakian Daniela Hantuchova.
While Williams continues to dominate the WTA Tour, no American man has reached the past five Grand Slam quarterfinals.
But it's Taylor and the two-time defending champion Penn State Nittany Lions with the edge heading into the quarterfinals.
Wells scored a career-high 30 points and Maryland upset Duke 83-74 on Friday night in the ACC tournament quarterfinals.
Her second tournament came at the French Open, where she reached the quarterfinals.
Serbia's Novak Djokovic, the top seed, was facing American Sam Querrey for a place in the quarterfinals later Thursday.
Roddick made the announcement after beating Richard Gasquet of France 6-3 7-6 in the quarterfinals of the Brisbane International.
Dunga was sacked after Brazil were sent crashing out of the quarterfinals of the World Cup by the Netherlands.
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That includes their 127-117 six-overtime victory over the Huskies in the 2009 quarterfinals.
The world No. 3 will next play Japan's Kei Nishikori, who he beat in last year's Australian Open quarterfinals.
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