Mrs McConville was shot dead by the IRA, as they wrongly believed she had passed information on to police. Ultimately claims that she was a police informant were dismissed after an official investigation by the Northern Ireland Police Ombudsman.
Her body was finally recovered from a beach in County Louth in 2003.
Mr Adams reported to a police station Wednesday for questioning. At the Antrim police station he was arrested and spent last night in custody.
Mrs McConville's son Michael, who was 11 when she was kidnapped has welcomed Adams' arrest. For the family any justice has been a long time coming. He later said "If the IRA hadn't have killed our mother, God knows, she still might have been alive today." On June 7 Mrs McConville would have been 80.
BBC News reorts:
He was arrested under the Terrorism Act 2000 and could be held until Friday evening, 48 hours after his arrest,at which time the police would have to contact a judge to seek an extension. Under the terms of that act, he could be held for a maximum of 28 days before being charged.
Opinion: How callous? A young family already mourning the loss of their father, losing a Mum in such tragic circumstances. Their home stability gone. Add to this not being able to hold a funeral for her for 31 years and the pain they suffered is unimaginable.
And in the end she was innocent of accusations made by a terror organisation.