Mother Rachel Fee and her partner Nyomi have been found guilty of murdering Rachel's two-year-old son Liam in Fife.
The couple were convicted of assaulting and killing the young child at his home in Thornton in March 2014. They had blamed another boy for the murder.
They were also convicted of a catalogue of abuse against two other children.
The jury returned a majority verdict after a seven-week trial at the High Court in Livingston. The couple are due to be sentenced on 6 July.
The jury found that Rachel and Nyomi Fee had subjected the toddler to an escalating pattern of cruelty during his short life.
The couple, originally from Ryton, Tyne and Wear, remained impassive as the jury found them guilty of all the charges against them.
Liam Fee's father, Joseph Johnson, was in tears at the verdict and had to be consoled by friends.
The jury were excused from duty for 10 years.
In the days before his death, Liam suffered a broken leg and arm. He was killed by a blow to his abdomen which was so severe that it ruptured his heart.
In total, he was found to have more than 30 injuries.
The couple had blamed another boy for Liam's death. However, during several interviews with specially-trained officers and a social worker, it became clear that the boy had not strangled or suffocated Liam.
He had put his hand over the toddler's mouth several days before his death but Liam had been walking and talking afterwards.
But the jury found Nyomi and Rachel to be jointly responsible for Liam's murder.
In addition, they subjected two other boys to a series of physical and psychological abuse over two years - including forcing one to sleep in a makeshift cage and another to sleep in a room with rats and snakes which they said "ate little boys".
Social services had been alerted to the Fees but had failed to take any action.
His nursery had alerted social services, worried by a change in Liam, and the fact that he was losing weight and had a number of injuries.
Liam's childminder had also made her concerns known.
A senior Fife social worker admitted to the court that at one point Liam "fell off their radar".
Fife Child Protection Committee is to carry out a significant case review.
Elaine Torrance, the president of Social Work Scotland, said such cases were "exceptional".
"Liam's death is an absolute tragedy and the level of cruelty that Liam experienced was deeply shocking," she said.
"What makes it worse is that the abuse was carried out by the very people Liam should have been able to trust the most: his mum and his step-mum."
Det Insp Rory Hamilton, of Police Scotland, said: "During joint interviews with specially-trained detectives and officials from Fife Council, the evidence began to build towards a picture of horrendous abuse which directly contributed to the version of events being put forward by the two accused being utterly discredited.
"This was a complex, challenging and sensitive investigation which involved interviewing two young children to establish the level of abuse and neglect both they and Liam Fee had been subjected to.
"It was because of their courage that detectives were able to identify Rachel and Nyomi Fee as being responsible for a wide range of serious offences against three children."
Sean Catherall, a former friend of the Fees, gave evidence at the trial.
He said he had lost touch with the couple after the abuse started and had not been aware of what was going on.
"Words cannot describe how much I actually physically hate them now. They've wrecked so many people's lives," he said.
"I didn't think in a million years she [Nyomi] was capable of any of that stuff, especially towards a baby - it kills us every day."