Five three-year-olds are among the thousands of children recorded by Police Scotland in the past two years, according to details released to the BBC after a freedom of information request.
Twenty four-year-olds and 376 children aged under eight - the age of criminal responsibility - are included in the figures.
Chief Inspector Hilary Sloan, of Police Scotland, said officers have to record all offences.
"The police record crimes because we have to have an understanding of what crimes are occurring within the communities and because of the Scottish Crime Recording Standard we have a responsibility to do that," she said.
Offences linked to the young children include shoplifting and vandalism.
Among all children under 16, there were 44,341 offences recorded.
In 2013-14 alone there were 5,154 violent crimes and 409 sexual crimes recorded among under-16s.
Although the age of criminal responsibility remains eight, the age at which children can be tried in a court of law is 12.
A Scottish Government spokeswoman said youth crime has fallen by 52 per cent over the last five years and continues to fall, dropping 22 per cent since 2011-12.
"The Scottish Government's early intervention initiative, the whole system approach, tackles all aspects of youth offending from low level crime to the most serious and harmful offences and aims to stop young people following the wrong path into a life of crime by identifying at the earliest opportunity when they are in trouble," the spokeswoman said.
"Police, courts, education and social services work together to address minor offending behaviour before it becomes a major problem. This approach was first piloted in Aberdeen in 2010 to 2011 and saw marked improvement in youth offending with youth crime down 20 per cent and offence referrals to the Children's Reporter falling 40 per cent.
"The Scottish Government will consider whether the age of criminal responsibility should be raised within the lifetime of this Parliament. We have set up a working group to look at the challenges of doing so."