Here we take a look at nine cases for which nobody is yet behind bars. They include stabbings, a shooting and some brutal attacks.
One of the victims was just 13 when she was sexually assaulted, strangled and left naked at the foot of a manure heap in May 1964.
Another victim was 80 when she was found strangled in the kitchen of her home in the village of Grimethorpe, near Barnsley, on January 24, 2002.
One of the most recent cases is that of a 21-year-old who died after being stabbed in the chest in an alleyway off Langsett Walk, Uperthorpe, on August 14, 2018.
Detectives have named a man they are keen to speak to but he has gone to ground.
All his friends, relatives and acquaintances have been served with harbouring notices by the police, meaning that if they are caught helping him to evade arrest they could be prosecuted.
A tiny piece of information could be just what the police need to crack a case – it could be the missing piece of the jigsaw they are looking for.
Anyone with information on any of the murders listed here should contact South Yorkshire Police on 101 or Crimestoppers, anonymously, on 0800 555111.
5. Michaela Hague - 2001
Mum Michaela Hague, who was a sex worker, was stabbed and left for dead on waste ground in Spitalfields on November 5, 2001. Photo: JPI Media
6. Dawn Shields - 1994
The body of 19-year-old Dawn was found in a shallow grave in the Peak District on May 20, 1994. She had been strangled. Photo: JPI Media
7. Kavan Brissett - 2018
Kavan Brissett died after being stabbed in the chest in an alleyway off Langsett Walk on August 14, 2018. Prime suspect Ahmed Farrah, also known as Reggie, is still on the run. Photo: JPI Media
8. Jonathan Motondo - 2007
Jonathan Matondo was shot dead in a killing which shocked Sheffield and blew the lid off a deadly feud in which rival gang members from Burngreave and Pitsmoor were at war. Photo: JPI Media