[3] Upon graduation from law school, Eskridge served as a law clerk to Judge Charles Clark of the United States Court of Appeals for the Fifth Circuit and to Justice Byron White of the Supreme Court of the United States.

He previously spent over two decades in the Houston, Texas, office of Susman Godfrey and then was partner at Quinn Emanuel Urquhart & Sullivan.

[3] Eskridge serves as an adjunct professor at the University of Houston Law Center, teaching a course on the origins of the federal constitution.

President Trump nominated Eskridge to the seat vacated by Judge Gray H. Miller, who assumed senior status on December 9, 2018.

[7] On October 16, 2019, the United States Senate invoked cloture on his nomination by a 61–29 vote.