Celebrated Hollywood filmmaker Rob Reiner and his wife, producer Michele Singer Reiner, were found dead in their Brentwood, California, home on Sunday.

Their son Nick Reiner, 32, was arrested in Los Angeles on Sunday and is being held on suspicion of murder. Police have said the couple were victims of homicide, and prosecutors are reviewing the case, weighing whether to bring charges against him.

Rob Reiner, who was known for directing movies such as This is Spinal Tap and When Harry Met Sally, had two sons and a daughter with his wife of 36 years.

Here’s what we know about Nick Reiner, their younger son, and the investigation so far.

The couple’s youngest child, daughter Romy, found their bodies in their home in Brentwood, a celebrity enclave full of mansions, boutique shops and restaurants on the westside of Los Angeles, multiple sources confirmed to the BBC’s US media partner CBS News.

The Reiners had suffered multiple stab wounds, it reported. Their cause of death has not officially been released.

Two sources also told CBS News that Rob and Nick Reiner had engaged in a brief but loud argument during a party the previous evening.

Nick Reiner is currently in custody after being arrested on Sunday, according to Los Angeles County Sheriff’s Department records.

He was “booked for murder”, Police Chief Jim McDonnell said on Monday, and remains in custody with no bail. LA County Sheriff’s jail records previously said he was being held with bail set at $4m (£3m).

In a statement, police said that after their initial homicide investigation at the Reiners’ home, it was “further revealed” that Nick Reiner “was responsible for their deaths”.

Theories about a possible motive have bounced around social media. In comments that have spurred condemnation from both side of politics, President Donald Trump linked Rob Reiner’s death to what he calls “Trump Derangement Syndrome”, a term he often uses to describe his critics.

However, no alleged motive for the killings has been disclosed.

According to CBS News, Nick Reiner is being represented by celebrity defence attorney Alan Jackson, who represented disgraced Hollywood mogul Harvey Weinstein in his Los Angeles rape case.

Nick Reiner was expected to appear in court on Tuesday but Jackson told CBS that his client will not appear because he has not been “medically cleared” to do so.

A spokesperson for the LA County District Attorney Nathan Hochman told the BBC on Tuesday that “he’s a medical miss out”.

The spokesperson confirmed that prosecutors are reviewing the case and weighing charges.

The family openly discussed Nick Reiner’s long struggle with substance abuse ahead of the release of his semi-autobiographical 2015 film, Being Charlie. The father and son had teamed up to write and direct the movie about a teenager addicted to drugs and his difficult road to recovery.

Rob and Michele Reiner said that they had felt desperate during their son’s struggles, but when he would tell them that a rehab programme wasn’t working, they didn’t always listen and took the word of the professionals treating their son. He was in and out of rehab centres for years and experienced homelessness as a teenager.

“We were so influenced by these people. They would tell us he’s a liar, that he was trying to manipulate us. And we believed them,” Michele told the Los Angeles Times in 2015.

Rob Reiner added: “We listened to them when we should have been listening to our son.”

The film appeared to provide healing for the family. Rob said that by the time they started making the movie, their relationship “had gotten so much closer”.

Likewise, Nick Reiner told Variety at the time that their relationship grew during the process. Although he loved working with his dad on the film, he added that he wanted to be independent and complete his own projects.

Rob Reiner was previously married to late filmmaker Penny Marshall and adopted her daughter, Tracy Reiner, 61.

He met Michele Singer on the set of When Harry Met Sally, and a few years later they had their first son, Jake.

In a 1998 interview with the BBC right before his daughter Romy was born, he reflected on parenthood, saying that his approach to child-rearing was changing and through his experiences with his sons – Jake was six and Nick was four – he was “learning about being a parent”.

That same year, Reiner helped pass an initiative to use revenue from cigarette taxes for prenatal and early childhood support programme called First Five California.

“I’m trying to improve the fabric of society by making an investment early on with children, so that we will have a reduction in crime and teen pregnancy and drug abuse and child abuse.”