Medieval theology actually distinguished two conditions carrying the name limbo, from the Latin limbus, edge or border, and conflating them is a common source of confusion.
The limbo of the fathers (limbus patrum) held the righteous dead of the time before Christ, Abraham, Moses, the prophets, who could not yet enter heaven because Christ had not yet opened it. This limbo was understood to be emptied at Christ's death, when, in a reading built on 1 Peter 3:19 and the Apostles' Creed's confession that Christ "descended into hell," he went to proclaim his victory to "the spirits in prison" and led the righteous dead to glory. This is the harrowing of hell depicted throughout medieval and Byzantine art, and it is temporary and completed by definition; nothing remains for it to hold after the resurrection.
The limbo of infants (limbus infantum or puerorum) is the separate and much more disputed hypothesis discussed elsewhere in this collection: a permanent natural happiness proposed for infants who die without baptism, neither punished nor admitted to the vision of God. Unlike the limbo of the fathers, it was never resolved by any event internal to the story and remained an open theological opinion rather than a settled teaching.
Eastern Christianity did not develop either concept in Western terms. Orthodox theology affirms the descent to Hades and its associated deliverance but has generally not systematised a corresponding doctrine for unbaptised infants, tending instead to leave their fate to God's mercy without proposing an intermediate state, a reticence closer to the Catholic magisterium's own eventual caution than the confident medieval elaboration was.