Police suspect the children are with their father, 30-year-old Israel Hernandez, and his girlfriend, Martha Torres, who is the mother of the youngest missing child.
Hernandez has harmed the children before and may do so again, according to police, who said Hernandez and Torres picked up the kids from their aunt's home at 10 p.m. Sunday, and never returned.
Capt. Tom McLachlan said West Valley City police were not informed of the missing children until Monday afternoon, giving Hernandez a head-start of more than 12 hours.
McLachlan said Hernandez is a native of the Mexico City area, and he might be taking the children there.
Hernandez lost custody of the children, ages 3, 4 and 6, after what police called "severe physical abuse" that resulted in bruising and bleeding. The children were in the custody of their aunt, who occasionally allowed Hernandez to take the children without supervision for short periods of time.
The mother of the two oldest children has been out of the family picture for several years, according to police.
Police do not normally issue Amber Alerts for custody cases, but this case is different due to Hernandez's history and the potential threat to the children, McLachlan said.
"There's no indication that he's been to any parenting classes or anything else," McLachlan said. "So we believe this abuse immediately, or at some point, will start again."