Durst's troubled history with the law, and his alleged involvement in up to three murders, prompted a movie and then an HBO series about his life.
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The case spans the country and more than three decades. Here is a timeline highlighting some key events in the various cases he was connected to.
1973: Robert Durst, the son of New York real estate developer Douglas Durst, married a dental hygienist named Kathleen "Kathie" McCormack.
1980: The couple separated, but did not formally divorce, and according to People, he started dating Mia Farrow's sister Prudence, who was the subject of the Beatles song "Dear Prudence."
READ ALSO: Former friend claims Robert Durst attacked him with pointy boots in 1981
Jan. 31, 1982: By early 1982, the couple were living in different apartments in Manhattan, but still shared a cottage in Westchester County, New York, according to a People magazine article about the search for Kathie.
Kathie's friend Gilberte Najamy had a party in Newtown, Connecticut, on the night of Jan. 31, but Kathie left after receiving an angry phone call from her estranged husband.
"She came to the house, she was visibly upset. Things were not going well that weekend. She made phone calls back and forth to Bob, Bob would call the house 'I want you home now.' She didn't want to go," Najamy told ABC News in 2001.
"The last conversation that I had with Kathie was a very powerful conversation and as she was leaving my house, she turned to me and said 'Gilberte, promise me if something happens to me, you'll check it out. I'm afraid of what Bobby might do,'" she told ABC.
Durst told investigators that they got into an argument that evening when she arrived back at their South Salem, New York cottage, but that he drove her to the train station and she headed back into Manhattan. Five days later, Durst contacted police to tell them Kathie was missing.
According to People, an employee at Kathie's building thought he saw her from behind the day after Durst said she returned to Manhattan, and the dean of the medical school where Kathie was studying said he received a call from a woman identifying herself as Kathie who said that she was sick and was going to be missing class.
2000: Westchester County investigators re-opened their investigation into Kathie Durst's disappearance, which at that time was still ruled a missing persons case rather than a murder. The next year, Kathie was declared dead, though, her body was never found.
Investigators were scheduled to speak to Susan Berman, a good friend of Durst who lived in California. But on Christmas Eve, just days before her scheduled meeting with investigators, Berman was found in her home fatally shot in the back of her head.
According to a 2001 New York Times article, Berman's family and friends did not suspect Durst at the time and felt that he would never hurt Berman, who he was so close to that he gave her away at her wedding in 1984.
The Los Angeles Police Department said that Berman's death has been an open investigation ever since.
READ ALSO: Robert Durst linked to 1971 disappearance of college student
October 2001: Durst was arrested in Galveston, Texas, for the murder of Morris Black, his 71-year-old neighbor who was found dismembered.
Once police start looking into the murder, they discovered that Durst had rented an apartment in Galveston in April, according to The New York Times. He had told the landlord that he was renting the home for his mute sister-in-law, and gave the name of one of his childhood classmates. Durst was seen dressed up as a woman at the library and at local restaurants.
Durst was charged with the killing of Black, but claimed that he did so in self-defense.
READ MORE: Prosecutors: Robert Durst lived life as 'Dorothy' in Galveston
During the 2003 trial, the Associated Press reported that Durst admitted to using a paring knife, two saws and an ax while he was dismembering Black's body, which he later dumped in Galveston Bay. A jury later acquitted Durst.
2004: The AP reported that Durst pleaded guilty to bond jumping and evidence tampering. He was released on parole in 2005. After that, however, he had another run-in with the law when he violated the terms of his parole by returning to the home where he killed Black, which resulted in him having to spend four more months in jail.
2010: His case received renewed attention when a movie titled "All Good Things" was released detailing a fictionalized version of Durst's life, with the Durst character being played by Ryan Gosling. Durst contacted the film's director after its release, and their ensuing interactions result in an HBO series.
July 2014: Durst was arrested in July of 2014 for exposing himself and urinating on a candy display at a CVS pharmacy on Kirby. He later pleaded no contest to a criminal mischief charge and was ordered to pay restitution to CVS.
READ MORE: Video allegedly of Robert Durst urinating at Houston CVS released
March 15, 2015: Durst, 71 at the time, was arrested by FBI agents at a New Orleans hotel, a day before the final episode of the HBO series aired.
FBI agents believed Durst may have wanted to flee the country, possibly to Cuba, as he registered under an alias at the hotel, paid with cash, and was found with fake documents, a source told ABC News. The same day marked the first nonstop flight from New Orleans to Cuba since 1958.
"As a result of investigative leads and additional evidence that has come to light in the past year, investigators have identified Robert Durst as the person responsible for Ms. Berman's death," the Los Angeles Police Department said in a statement.
In the HBO series, Durst appeared to have admitted to the killings of Berman and his wife, and was heard on audio tape saying that he "killed them all, of course." The audio recording was captured on a microphone he was wearing while he was in the bathroom. The filmmakers said they didn't discover the audio until years after it was recorded.
March 16, 2015: Durst waived his right fight to extradition in a New Orleans courtroom. The Los Angeles district attorney charged him with one count of first-degree murder with the special circumstances of murder of a witness, as well as lying in wait and gun use allegations.
The charges carry the death penalty.
"Let me just say that we came here to waive jurisdiction and to go back to California and to get it on," said Durst's lawyer Dick DeGuerin, who represented him in the 2003 case relating to Black's death.
Durst was later arrested again in Louisiana on two newer charges: convicted felon in possession of a firearm and possession of a weapon with a controlled dangerous substance, which was a small amount of marijuana.
The Associated Press contributed to this report.