Craig Carter is the domestic abuser and murderer of his wife Ellen. Craig and Ellen would get into fights, screaming and cussing at each other, with Craig putting Ellen through the worst emotional and physical abuse. Olivia Benson intervened during her dispatch days when she was called by a neighbor.
Horrified by Craig's smug demeanor, she took Ellen aside and told her to defend herself next time, leaving out of protocol due to not seeing Ellen with physical wounds. Benson was scarred after she had to arrive to another call to the Carters a month later, seeing Craig kill Ellen by repeatedly crushing her head into a wall. That exposure would shape Benson's perspective of domestic violence and misogyny to firmly believe women's accounts of abuse and violence from partners.
Craig was presumably arrested and imprisoned on murder and domestic violence charges. (SVU: "Part 33")