Before deciding to convict him on all three charges, the jury heard about Mr. Biden’s spiraling addiction to crack cocaine from women in his life, as well as in Mr. Biden’s own words, which the prosecution shared by using excerpts from the audiobook of his memoir.

Here are some takeaways.

The verdict comes amid questions about the intersection of politics and the justice system.

The verdict in Mr. Biden’s trial came just weeks after former President Donald J. Trump was convicted in a Manhattan courtroom of falsifying business records to cover up a hush-money payment to a porn star. Both trials were surrounded by partisan dynamics and questions about the criminal justice system’s ability to operate without regard to politics.

Mr. Biden’s trial was held in the Biden family’s hometown, in the middle of a presidential campaign and amid intense pressure from Republicans to find criminality by Hunter Biden. The fact that juries have now convicted both the presumptive Republican presidential nominee and the son of his opponent, the sitting president, will not end debate about politics and the courts. But it might keep the issue from becoming further inflamed.

The trial has been a painful reminder of the struggles the Biden family has weathered over decades.

In his 2021 memoir, Hunter Biden laid bare his unrelenting abuse of crack cocaine. Witness testimony and text messages added to the damaging portrait of the president’s son, a stark reminder of his yearslong troubles at a time when his father is in a close re-election race.

Former romantic partners of Mr. Biden’s testified about his drug use, his coast-to-coast partying, his drug dealers in Washington, Delaware and California, and his daily cash withdrawals, typically more than $1,000 each time.

But testimony from his oldest daughter, Naomi Biden Neal, was perhaps the most emotionally wrought. Taking the witness stand on Friday in her father’s defense, she delivered a positive appraisal of his demeanor days after he bought the gun, describing him as “hopeful” and sober. But under cross-examination, that assessment seemed to falter, with prosecutors referring to text messages between her and Mr. Biden during that period that revealed an anguished relationship in which she struggled to connect with him while he was visiting New York, where she lived. Prosecutors suggested it was because he was using crack cocaine.

Each day of Mr. Biden’s trial, several of his family members sat behind the defense table, offering support by showing up alone or with hugs and kisses during breaks. The first lady, Jill Biden, was in the courtroom for most of the proceedings, cutting short a visit to France with the president to briefly return. After his guilty verdict, Hunter Biden left the courthouse on Tuesday holding her hand.

The verdict could affect any sentence from his coming trial on tax charges.

In September, Mr. Biden is scheduled to go on trial in Los Angeles for charges that he evaded a tax assessment, failed to file and pay taxes, and filed a false or fraudulent tax return. It is considered the more serious case against him.

The guilty verdict in his gun case on Tuesday raises the possibility that he would receive a stiffer sentence if a jury convicts him in the tax case because federal guidelines take into account previous convictions.

The special counsel, Mr. Weiss, in remarks on Tuesday reiterated that he brought the gun case because nobody “is above the law,” while also suggesting that the government would not seek a sentence more severe than for any other person convicted in such a case.

Like the gun charges, the indictment for the tax-related offenses chronicles Mr. Biden’s years of drug abuse and cites a wild spending spree. “Between 2016 and Oct. 15, 2020, the defendant spent this money on drugs, escorts and girlfriends, luxury hotels and rental properties, exotic cars, clothing, and other items of a personal nature, in short, everything but his taxes,” prosecutors wrote in bringing charges.

The gun trial put some of that behavior on display, but the tax charges span a longer time period. That trial is set to start on Sept. 5, about a month before he is expected to be sentenced for the gun crimes.

The trial shows how the government’s strategy for keeping guns out of the wrong hands relies on a single form.

During his opening statement, one of the prosecutors, Derek Hines, cited the form as the way to keep guns out of the wrong hands. “That form in a background check is the only safeguard that exists to screen whether someone can lawfully own a firearm,” he said. “Background checks are one of the few protections that exist when it comes to having guns.”

Mr. Biden’s lawyer, Abbe Lowell, made a similar point, noting that alcohol is not even mentioned on the form.

“The law in this case does not prevent, and the form does not ask if someone is an alcoholic,” Mr. Lowell said. “Under the law, and the form in this case, a person can even be drunk and still, under this law and this form, be able to walk in a gun store and buy it.”

The case against Mr. Biden is unusual, and not just because he is the son of a sitting president.

People accused of lying on a federal firearms application are typically not indicted on that charge alone, making Mr. Biden’s case unusual in that it would rarely reach a jury.

Typically, it would be part of a suite of charges that include a more serious crime. In many cases, people facing those charges negotiate deals for probation and participation in programs that include counseling and regular drug testing.

There are fewer than about 300 prosecutions a year for lying to a federally licensed firearms dealer. Some 25 million to 30 million background checks were performed annually around the time of Mr. Biden’s gun purchase, according to statistics obtained by The Washington Post.