The Menendez brothers have fought a decadeslong battle for freedom since being convicted in 1996 in the sensational murders of their parents at the family’s Beverly Hills home.

For years, they made little progress.

But a series of events in the past year has brought them closer to their goal after spending 34 years behind bars.

There is no question they killed their parents. But they long have claimed that the outcome of the case would have been different had the jury been allowed to hear evidence that they were sexually molested by their father.

Now Los Angeles County District Attorney George Gascón says he’ll investigate new evidence related to those claims.

The process could pave the way for the brothers to be retried, resentenced to a lesser prison term or released from custody. Gascón said he has not made a final decision.

Why now?

There has been intense focus on the case in recent years.

• Attorneys for the brothers filed petitions citing new evidence related to the molestation claims.

• In a documentary, a former member of the boy band Menudo said the Menendezes’ father molested him.

• Family members have rallied to get them released.

• A new hit Netflix miniseries has focused more attention on the case.

• Some have argued that times have changed, and that the brothers’ allegations of abuse might have been received differently at trial today.

• Kim Kardashian, a celebrity who also has become a prison reform advocate, called on officials to release them. “We owe it to those little boys who lost their childhoods, who never had a chance to be heard, helped or saved,” she wrote in a piece for NBC News.

What do we know about the killing?

In 1989, Erik and Lyle Menendez bought a pair of shotguns with cash, walked into their Beverly Hills home and shot their parents while they watched a movie in the family living room. Prosecutors said Jose Menendez was struck five times, including in the back of the head, and Kitty Menendez crawled on the floor wounded before the brothers reloaded and fired a final fatal blast.

It was a sensational murder case that captivated the nation.

Initially, police speculated the killings were a Mafia hit based on the gruesome scene in the home. Erik and Lyle Menendez eventually were charged with murder after Erik, who was then 18 years old, confessed the killings to his therapist in March 1990.

What happened in court?

Prosecutors argued that the brothers’ motivation in the killings was a simple one: to gain access to their parents’ multimillion-dollar estate. But the brothers’ defense attorneys countered that years of violent sexual abuse at the hands of their father preceded the shootings, justifying the killings as a form of self-defense.

The first trial ended with two hung juries. In the second, allegations of abuse and supporting testimonies were restricted, and Lyle and Erik Menendez were convicted of first-degree murder in March 1996.

After their convictions, the brothers pursued unsuccessful appeals.