Ms Wallace, who worked as a nurse at Hunters Hill Private Hospital, disappeared after a night out with friends at a Crows Nest bar on Sydney's north shore on September 24, 1983.

But after a major development in technology, her alleged killer Robert Adams was arrested after police were able to match two hairs found in the boot of his brown Holden Commodore sedan with hair taken from Ms Wallace's hairbrush.

On Tuesday, 33 years after Ms Wallace's disappearance, Adams sat in the dock of the NSW Supreme Court at the start of his judge-alone murder trial.

Crown prosecutor Mark Hobart, SC, told the court that an intoxicated Ms Wallace was last seen by friends getting into Adams' car about 4am on Saturday September 24, 1983.

Mr Hobart outlined how Adams had violently raped three other women and attempted to strangle them in the lead up to Ms Wallace's disappearance.

Adams, a carpenter who worked at the Lane Cove National Park, was originally arrested in September 1983.

At the time of his arrest he told police that he had met Ms Wallace at the Alpine Inn bar and had a number of drinks with her before he offered to take her home.

He said he pulled the car over shortly after turning off Willoughby Road and the pair began kissing and "playing with each other sexually" before he climbed on top of her in the passenger seat.

Adams explained he could not remember if the pair had sexual intercourse but at some stage he climbed back into the driver's seat of his car and fell asleep.

When he awoke Ms Wallace was gone.

The accused then drove to his Chatswood apartment before attending a champagne breakfast at St Leonards.

During his police interview he also explained to police that on the afternoon of Monday, September 26 he stayed home and washed both his car seats because the passenger seat "had cum on it and it smelled".

Mr Hobart also told the court about the evidence of Adams' flatmate Suzanne Beckingham - who noticed two brown coloured seat covers hanging on the clothes line outside her flat the day after Ms Wallace's disappearance.

Ms Beckingham has said she saw Mr Adams washing the boot of his car with rags and a hose. He also had a vacuum cleaner with him.

"Beckingham had never seen him do this before," Mr Hobart said.

In October 1983, police seized Mr Adams' car and vacuumed the boot and collected material.

The court heard how the case was re-opened by the NSW Police unsolved homicide squad in 2008, and in 2013 the hairs originally collected from the boot of Mr Adams' car were tested along with hair found from Ms Wallace's hairbrush which was located in her Drummoyne apartment.

On Friday, December 20, 2013, Adams was arrested and charged with murder.

He denied murdering Ms Wallace and reiterated the statement he gave to police in 1983.

Mr Adams' lawyer told the court that the accused denied choking the deceased and that there would be a dispute about the DNA evidence and some of the tendency evidence.

Despite extensive searches, the body of Ms Wallace has never been found

The trial continues before Justice Richard Button.