One of four children, Durst grew up in Scarsdale, New York. He is the son of real estate investor Seymour Durst and his wife Bernice Herstein. His siblings are Douglas, Thomas, and Wendy. Durst's paternal grandfather, Joseph Durst, a penniless Jewish tailor when he emigrated from Austria-Hungary in 1902, eventually became a very successful real estate manager and developer, founding the Durst Organization in 1927.

Durst attended Scarsdale High School, where classmates described him as a loner. He earned a bachelor's degree in Economics in 1965 from Lehigh University, where he was a member of the varsity lacrosse team and the Business manager of The Brown and White student newspaper. He enrolled in a doctoral program at UCLA later that year, where he met Susan Berman, but eventually withdrew from the school and returned to New York in 1969. Durst went on to become a real estate developer in his father's business; however, it was his brother Douglas who was later appointed to run the family Business in the 1990s. The appointment caused a rift between Robert and his family, estranging him from them.

Schulze, a Middlebury College freshman, patronized Durst's health food store on December 10, 1971, the day she disappeared, and was last seen that afternoon near a bus stop across from the store. DeGuerin characterized the Schulze investigation as "opportunistic" and said he would not permit his client to be questioned by Vermont police. Author and investigative Journalist Matt Birkbeck reported in 2003, and again in his 2015 book A Deadly Secret, that credit card records placed Durst in Eureka on November 25, 1997, the day Mitchell vanished. Mitchell may have volunteered in a homeless shelter that Durst frequented; Durst, dressed in women's clothing, had visited the Eureka shoe store owned by Mitchell's aunt. Mitchell was last seen walking to work from her aunt's store and possibly speaking to someone in a stopped car; a witness Sketch of Mitchell's presumed abductor resembles Durst.

On April 12, 1973 – Durst's 30th birthday – he married Kathleen McCormack. Durst divorced her in 1990, eight years after her disappearance, claiming spousal abandonment. On December 11, 2000, shortly before the Berman killing, Durst married Debrah Lee Charatan. According to The New York Times, the couple briefly shared a Fifth Avenue apartment in 1990 but "have never lived together as husband and wife". Durst once told his sister that it was "a marriage of convenience"; "I wanted Debbie to be able to receive my inheritance, and I intended to kill myself," Durst said in a 2005 deposition. Charatan currently lives with one of Durst's lawyers, Steven I. Holm.

Seymour became head of the family Business in 1974 upon Joseph's death. Durst claimed that, at the age of seven, his father walked him to a window where he saw his mother on the roof of the family's Scarsdale home prior to her death, which resulted when she fell or jumped. In a March 2015 New York Times interview, his brother Douglas denied this. As children, Robert and Douglas underwent counseling for sibling rivalry; a 1953 psychiatrist's report on ten-year-old Robert mentioned "personality decomposition and possibly even schizophrenia".

In the early 1980s, Durst owned a series of seven Alaskan Malamutes each named Igor, which according to his brother Douglas all died under mysterious circumstances. In December 2014, prior to the airing of The Jinx, Douglas told The New York Times that, "In retrospect, I now believe he was practicing killing and disposing [of] his wife with those dogs." Durst was once recorded saying he wanted to "Igor" Douglas. Durst, however, has disputed the notion that he owned seven dogs named Igor; he owned three, he said, one that was run over and another that died in surgery after eating an apple core, "before the Igor that lasted forever."

In late 1981, while Durst was still married to McCormack, he was nearing the end of a three-year affair with Prudence Farrow, who was also married at the time. A few months before McCormack's disappearance in January 1982, Farrow called her and asked that she give him up, as friends said she wanted him all to herself. After Durst's acquittal of murdering Black in 2003, Farrow contacted law enforcement authorities with concerns for her safety, as she said Durst was angry with her for terminating their relationship three days before McCormack disappeared.

Shortly before her disappearance, McCormack was a student in her fourth and final year at the Albert Einstein College of Medicine in The Bronx and was only a few months short of earning her degree. She had intended to become a pediatrician. McCormack was last seen by someone other than Durst the evening of January 31, 1982, at a friend's dinner party in Newtown, Connecticut. Later on that night, McCormack unexpectedly arrived at the house of her best friend, who noticed she was upset and was wearing red sweatpants, which the friend found odd since McCormack had often dressed in much better quality clothing. She later left for South Salem, New York, after a call from her husband. Although the couple argued and fought, Durst maintained that he put his wife on a train to New York City, had a drink with a neighbor, and spoke to his wife by telephone later that evening. "That's what I told police," Durst later told documentary filmmakers. "I was hoping that would just make everything go away."

Media have variously reported Durst's financial status as "real estate baron", "rich scion", "millionaire", "multimillionaire", and "billionaire". The Durst family's real estate holdings are worth more than $4 billion, but his brother Douglas was in control of the company beginning in 1994, shortly before their father's death. From about 1994 to 2006, Robert waged a legal campaign to gain greater control of the family trust and fortune. During that time he received $2 million a year from the trust. In 2006 the case was settled, with Durst giving up any interest in his family's properties and trusts in exchange for a one-time payment of about $65 million. It is unknown how much of that went to legal fees and taxes. Durst was still active in real estate; he reportedly sold two properties in 2014 for $21.15 million after purchasing them in 2011 for $8.65 million. At the time of his 2015 arrest, the FBI estimated Durst's net worth at approximately $100 million; The New York Times estimated his net worth at $110 million.

Days after the Berman murder, police were reportedly examining connections between Durst and disappearances of 17-year-old Lynne Schulze from Middlebury, Vermont, and 16-year-old Karen Mitchell from Eureka, California. Investigators are also looking into a possible connection with the disappearance of 18-year-old Kristen Modafferi, last seen in San Francisco in 1997.

The Associated Press reported that a March 1999 letter from Durst to Berman, discovered by her stepson and turned over to the filmmakers during their research, provided "key new evidence" leading to the filing of murder charges.

Durst said in a 2005 deposition that Berman called him shortly before her death to say that Los Angeles police wanted to talk to her about McCormack's disappearance. A study of case notes by The Guardian cast doubt on whether the LAPD had made such a call, or whether then-Westchester County District Attorney Jeanine Pirro had scheduled an interview with Berman at all. Durst moved to Galveston, Texas, in 2000, lived in a boarding house, and began posing as a woman to avoid police inquiries. Durst had been tipped off to the re-opened investigation into his wife's disappearance on October 31, 2000, and immediately began planning for life as a fugitive. Berman biographer Cathy Scott has asserted that Durst killed Berman because she knew too much about McCormack's disappearance.

On October 9, 2001, Durst was arrested in Galveston shortly after body parts belonging to his elderly neighbor, Morris Black, were found floating in Galveston Bay. He was released on $300,000 bail the next day. Durst missed a court hearing on October 16 and a warrant was issued for his arrest on a charge of bail jumping. On November 30, he was caught inside a Wegmans supermarket in Bethlehem, Pennsylvania, after trying to shoplift a chicken salad sandwich on pumpernickel bread, Band-Aids, and a newspaper, even though he had $500 cash in his pocket. A police search of his rented car yielded $37,000 in cash, two guns, marijuana, Black's driver's license, and directions to the Connecticut home of Gilberte Najamy, a former confidante of McCormack who had dogged Durst for years publicizing accusations he had murdered his wife. Durst also used his time on the run to stalk his brother Douglas, visiting the driveway of his home in Katonah, New York, while armed.

In mid 2002, Durst signed over a power of attorney to his wife Charatan, a real estate investor, and it is believed their holdings remain closely intermingled. In 2006, Durst gave Charatan around $20 million of his $65 million trust settlement.

In 2003, Durst was tried for the murder of Black. He employed defense attorney Dick DeGuerin and claimed self-defense; DeGuerin conducted two mock trials in preparation for the case. Durst's defense team had difficulty communicating with him, so they hired Psychiatrist Dr. Milton Altschuler to find out why. Altschuler spent over 70 hours examining Durst and diagnosed him with Asperger syndrome, saying, "His whole life's history is so compatible with a diagnosis of Asperger's disorder." Durst's defense team argued at trial that the diagnosis explained his behavior.

In 2004, Durst pleaded guilty to two counts of bail jumping and one count of evidence tampering. As part of a plea bargain, he received a sentence of five years and was given credit for time served, requiring him to serve three years in prison. Durst was paroled in 2005. The rules of his release required him to stay near his home; permission was required to travel. That December, Durst made an unauthorized trip to the boarding house where Black had been killed and to a nearby shopping mall. At the mall, he ran into former Galveston trial judge Susan Criss, who had presided over his trial. Due to this incident, the Texas Board of Pardons and Paroles determined that Durst had violated the terms of his parole and returned him to jail. He was released again from custody on March 1, 2006.

In 2011, Durst purchased a $1.75 million townhouse on Lenox Avenue in Harlem. A source close to his estranged family confirmed that he was living there at least some of the time, and they were keeping him under surveillance. Durst also owns three condominiums in a multi-story complex in Houston, and after filing suit, received a $200,000 settlement in 2006 from a Houston developer who refused to let him move into a unit newly purchased by his wife, which she had then immediately resold to Durst for $10. At the time of Berman's murder in Los Angeles, Durst had just sold a home in Trinidad, California, but maintained an office in Eureka while renting in nearby Big Lagoon.

In 2012 and 2013, Durst's family members sought and received restraining orders against him, claiming they were afraid of him. Durst was charged with trespassing in New York for walking in front of townhouses owned by his brother Douglas and other family members. He went on trial and was acquitted in December 2014. The judge also vacated the thirteen orders of protection his family members had taken out on him.

In July 2014, Durst was arrested after turning himself in to police following an incident at a Houston CVS drugstore in which he allegedly exposed himself without provocation and urinated on a rack of candy. He then left the store and casually walked down the street. Durst was charged with misdemeanor Criminal mischief. In December 2014, he pleaded "no contest" and was fined $500. His Lawyer described the incident as an "unfortunate medical mishap", as Durst had just been released from a hospital where he had undergone two medical procedures. The incident was recorded on videotape.

In November 2015, nearly 34 years after her disappearance, McCormack's three sisters and 101-year-old mother sued Durst for $100 million, citing his apparent role in her murder and his denial to her family of the "right to sepulcher", a New York law that grants immediate relatives access to a deceased person's body and the opportunity to determine appropriate burial. If successful, the lawsuit could deprive Durst of most or all of his inherited fortune. McCormack's brother James had attempted in October 2015 to file a wrongful death suit against Durst on behalf of his mother, but was challenged by one of his sisters, who holds her mother's power of attorney. DeGuerin commented that "there is no evidence that Robert Durst had anything to do with Kathleen's disappearance. Anybody can file a lawsuit, but eventually they'll have to come with evidence." On December 7, 2015, the same family members filed a suit asking the court to freeze Durst's assets. The family's attorney, Robert Abrams, called Durst the "poster child" for why courts block defendants from disposing assets while civil lawsuits are pending. In July 2016, the McCormick family asked the Surrogate’s Court in Manhattan to "declare that Kathie died on January 31, 1982, when she was murdered by her husband, Robert Durst" so the sepulcher lawsuit can proceed.

Durst's attorneys requested a later date for the federal weapons charge trial, saying they'd need more time to prepare after rulings on pending motions. U.S. District Judge Helen Berrigan later rescheduled the trial to January 11, 2016. On November 16, 2015, a New Orleans federal judge ordered Durst re-arraigned on the weapons charges and scheduled a hearing for December 17. When asked, Durst's attorney said only that Durst did not kill Berman, and that he wants to resolve the other charges to expedite Durst's extradition to Los Angeles to face that charge.