The list below features some of the most recent offences as well as a number of the most serious, historic crimes which detectives are still keen to solve.
1. MURDER
Mohammed Ali, Jamal Ali, Saeed Hussein and Ahmed Warsame are believed to hold vital information about the murder of 22-year-old Jordan Thomas who was shot dead on Derek Dooley Way, Sheffield, in 2014. Photo: JPI Media
2. MURDER
Ahmed Farrah, aged 30, is believed to hold vital information about the fatal stabbing of 21-year-old Kavan Brissett, who was knifed in Upperthorpe, Sheffield, last August. Photo: JPI Media
3. SEXUAL ASSAULT
This man is wanted over a sex attack in Barnsley town centre on July 14 when a 20-year-old woman was assaulted in Peel Street. Photo: JPI Media
4. WITNESS INTIMIDATION
Doyle James, with links to East Herringthorpe, Rotherham and Intake, Manor and Handsworth, Sheffield, is wanted for failing to answer bail and in connection to witness intimidation, malicious communications and breaching bail conditions. Photo: JPI Media