He graduated magna cum laude and Phi Beta Kappa with a bachelor's degree from Columbia in 1983. He received a Juris Doctor (J.D.) degree magna cum laude in 1986 from Harvard Law School, where he was an editor of the Harvard Law Review. After law school, Estrada served as a law clerk to Judge Amalya Lyle Kearse of the U.S. Court of Appeals for the Second Circuit. He then clerked for Justice Anthony M. Kennedy of the U.S. Supreme Court during his first year on the Court in 1988. One of his fellow clerks during that year was Peter Keisler, another nominee to the D.C. Circuit whose nomination is presently under consideration in the Senate of the 110th Congress.
From 1990 until 1992, Estrada served as Assistant U.S. Attorney and Deputy Chief of the Appellate Section, U.S. Attorney's Office, Southern District of New York. In 1992, he joined the United States Department of Justice as an Assistant to the Solicitor General for the Clinton Administration. In those capacities, Estrada represented the government in numerous jury trials and in many appeals before the U.S. Court of Appeals for the Second Circuit. Before joining the U.S. Attorney's Office, he practiced law in New York with Wachtell, Lipton, Rosen & Katz.
Estrada was married to Laury Gordon Estrada until her death at age 46 on November 28, 2004.
A bipartisan group of former Solicitors General wrote a letter objecting to the Democrats' demand for memos that Estrada had written while he was with the office. While not addressing past instances where such memos had previously been released, the letter argued release of prior memos by government employees to the public would endanger the Solicitor General Office's ability to provide confidential legal advice to the Executive Branch. Some observers claimed that the Democrats also wished to avoid giving Bush points with Hispanic voters. The Democrats hotly contested this; however, internal memos to Senate Minority Whip Dick Durbin mention liberal interest groups' desire to keep Estrada off the court because his Latino heritage made him "especially dangerous" as a potential future Supreme Court nominee.
On March 6, 2003, there was the first of several failed cloture votes on Estrada. Fifty-five senators voted to end debate on his nomination and allow a final confirmation vote, and forty-four senators voted not to end debate. After twenty-eight months in political limbo and a protracted six month long battle using the filibuster, Estrada withdrew his name from further consideration on September 4, 2003. Bush nominated Thomas B. Griffith in his place, who was confirmed in 2005.
Estrada is currently a partner at the Washington, D.C., law office of Gibson, Dunn & Crutcher LLP, where he is a member of the firm's Appellate and Constitutional Law Practice Group as well as the Business Crimes and Investigations Practice Group.