Gilstrap was born in Pensacola, Florida. He is an Eagle Scout. He received a Bachelor of Arts from Baylor University in 1978, where he graduated magna cum laude. As an undergraduate he was inducted into Phi Beta Kappa. He also earned a Juris Doctor from Baylor Law School in 1981, where he was associate editor of the Baylor Law Review. While on the review, he published the article Video Recorders: Copyright Infringement, 33 Baylor Law Review 695 (1981). Gilstrap later served as president of the Baylor Law Alumni Association.
After graduation from law school, Gilstrap entered private practice in the town of Marshall, Texas as an Associate with the firm of Abney, Baldwin & Searcy from 1981-1984. He later became a founding Partner of Smith & Gilstrap in Marshall from 1984-1989, where his practice covered oil and gas, real estate, probate law and occasionally patent cases. Among the patent cases Gilstrap worked on while at Smith & Gilstrap included defending Capital One Financial Corporation in a patent suit brought by LML Patent Corporation alleging patent infringement by several banks on patents covering payment services and the representation of a company called Bluestone Innovations Texas in a patent infringement suit brought against a number of foreign companies involving Light-emitting diodes (or LED) technology. Gilstrap served as a Harrison County Judge from 1989 to 2002. Judge Gilstrap also served 16 years on the Courthouse Preservation Council in Marshall, and also served as the Chair of the Unauthorized Practice of Law Committee with the State Bar of Texas. In 2004, Judge Gilstrap co-authored an article with Leland de la Garza which appeared in the Texas Bar Journal: UPL: Unlicensed, Unwanted and Unwelcome 67 Texas Bar Journal 798 (2004). While and after serving as a Harrison County Judge, Gilstrap was practicing at Smith & Gilstrap until he became appointed to the federal bench in 2011.
On May 19, 2011, President Barack Obama nominated Gilstrap to a seat on United States District Court for the Eastern District of Texas. "Throughout their careers, these nominees have displayed unwavering commitment to justice and integrity," stated President Obama in a press release about Judge Gilstrap's nomination, "[t]heir records of public service are distinguished and impressive and I am confident that they will serve the American people well from the United States District Court bench. I am honored to nominate them today." Gilstrap was rated as Unanimously Qualified by the American Bar Association and had a hearing before the Senate Judiciary Committee on July 28, 2011. On September 15, 2011, the Senate Judiciary Committee reported his nomination to the Senate floor by voice vote. The Senate confirmed his nomination by voice vote on December 5, 2011. He received his commission on December 6, 2011.
According to Lex Machina and other sources, Judge Gilstrap is the United States District Judge that hears the most patent cases in the country and has been referred to by many sources as the nation's single "busiest patent judge". In 2016, for example, 1,119 cases were brought before Judge Gilstrap, who saw more new cases than the next 10 highest ranking judges - 2016 was also the fourth year in a row where Judge Gilstrap had more patent cases than any other federal judge. In 2015, over 28% of the nation's patent cases were filed before him. Judge Gilstrap and United States Magistrate Judge Roy S. Payne, who are the only two judges based out of the Marshall division of the United States District Court for the Eastern District of Texas, also have the most patent cases filed before them out of the predominant share of the nation's patent cases that are filed in the Eastern District of Texas.
From 2014 to 2015, Judge Gilstrap was ranked first amongst all federal judges (either United States District Judge or United States Magistrate Judge) with the most patent cases filed before him. According to Docket Navigator, in 2015 Judge Gilstrap was also ranked first as to the single federal judge having to preside over the highest number of filed cases, the highest number of litigants, and the highest number of accusations. Also according to Docket Navigator, Judge Gilstrap is the top ranked (#1) most active federal judge (either District or Magistrate judge) by number of parties, number of orders and by number of cases from the years of 2014 to 2008 (even though he came on the bench in 2011) for patent litigation.
In 2013, Judge Gilstrap presided over the case of TQP Development v. Newegg where the jury ordered Newegg to pay $2.3 million for infringing four asserted claims in a patent involving modem technologies and Internet security systems such as SSL or TLS together with the RC4 Cipher. However in 2015, Judge Gilstrap ruled that Newegg did not infringe TQP Development's patent, effectively overturning the verdict.
In 2015, Judge Gilstrap ruled that a $533 Million jury verdict (the largest ever for a Patent assertion entity, Smartflash) in Smartflash, Inc. v. Apple be thrown out due to a faulty jury instruction, and ordered a new trial just on the issue of damages.
Also in 2015,Judge Gilstrap denied a request by ZTE Corporation for a new trial after a jury found that it infringed two patents owned by DataQuill covering data entry technology and awarded DataQuill $31.5 Million.
In 2015, Judge Gilstrap ordered 35 U.S.C. 285 "exceptional case" fees to be levied against a notorious Non practicing entity (the worst of them known as Patent trolls), eDekka LLC. He ruled that the case was "objectively unreasonable" after previously invalidating eDekka's patent under the U.S. Supreme Court case of Alice v. CLS Bank International.
In 2016, Judge Gilstrap enhanced damages based on a jury verdict that LG willfully infringed two Standard essential patents (SEPs) owned by Core Wireless covering cellular standards. He previously denied LG's motion for summary judgmement that the SEPs were not willfully infringed, letting that issue go to the jury.
In 2017, Judge Gilstrap levied sanctions against Patent assertion entity Iris Connex, which had a patent covering phone technology used to take "selfies". In his Order, Judge Gilstrap mentioned that due to the misconduct of the parties, this was "the clearest example of an exceptional case to yet come before" him.
In June 2017, Judge Gilstrap provided a four-part test in determining venue after the U.S. Supreme Court case of TC Heartland LLC v. Kraft Foods Group Brands LLC in the case of Raytheon v. Cray, but in September 2017 was overturned by the Court of Appeals for the Federal Circuit in response to a petition for writ of mandamus by Cray.