A team has been set up by Strathclyde Police to investigate about 35 murder mysteries.
The Bible John case is among those being re-examined
The Unresolved Case Unit has been tasked with re-examining crimes such as the notorious Bible John killings of three women in Glasgow in the 1960s.
Detectives hope new technology and scientific progress can now help to track down the murderers.
Investigators have said they will also be looking again at suspicious missing persons cases.
A number of criteria have to be met before an unsolved case is reopened.
Officers would need to know if evidence was still available and if the main witnesses involved were still alive.
The same condition would also apply to experts such as pathologists.
Detective Superintendent Kenny Watters said they would be looking at cases such as the Bible John murders and that it was not only forensic advances which could provide breakthroughs.
Mr Watters said: "People's allegiances may change over the years and if you're looking at cases from maybe 25, 30 years ago, people who provided alibi statements at that time, their circumstances might have changed, their allegiances might have changed.
"They may well now be willing to speak to the police and give the truth about what happened."
The first of Bible John's victims, Pat Docker, died in February 1968, followed by Jemima McDonald and Helen Puttock.
He met his victims at the Barrowland Ballroom, where he charmed them and often quoted passages from the Bible.
Bible John has never been caught, despite DNA tests
Some detectives at the time believed one murderer was responsible for all three deaths but other colleagues were not convinced.
It is one of Britain's most baffling murder riddles but police in Glasgow have never given up in the hunt for the serial killer.
The Bible John case returned in dramatic style to the public eye in 1996, when police exhumed for DNA tests the body of a man buried in a graveyard in Stonehouse, Lanarkshire.
They said later there was insufficient evidence from the tests to link him with the scene where Helen Puttock was murdered.
A number of suspects, in their 50s and 60s, gave DNA samples to police last year.
Dr Adrian Linacre, a lecturer in forensic science at Strathclyde University, said new processes can identify traces of evidence which previously could not be found.
He said: "Now with the advent of DNA profiling someone who's just held something for a brief period, or held someone, you're going to transfer your DNA."