Limbo is also a Catholic concept. The word is derived from the Latin limbus meaning edge or boundary and refers to the edge of “hell.” There are two basic ideas here. One is Limbo of the father’s and one is Limbo of Infants.

Limbo of the father’s was a temporary “limbo,” a place the Catholic Church taught that righteous men and women of the Old Testament went after death. This would essentially be the equivalent of what we might refer to as Abraham’s Bosom or Paradise (See Luke 16). The idea was prior to Jesus death and resurrection people could not go directly to heaven after death - since it was Jesus who makes eternal life possible. And so based on some OT passages, Jesus parable in Luke 16 about Lazarus, and a few other passages many believed that when someone died under the Old Covenant God provided a temporary paradise for them. But after the death and ascension of Jesus “taking captivity captive” there would be no more need for the limbo of the fathers since they would now be in heaven.

Limbo of Infants was, under Catholic doctrine, the permanent place of existence for all children who died in infancy before they were baptized. In some views it also included the mentally retarded. In the Catholic Church baptism is understood to be necessary for salvation, hence if a child is not baptized they could not go to heaven.

Some who held this Catholic theory regard the Limbo of Infants as a state of maximum natural happiness, others as one of "mildest punishment." Still others in the Catholic Church believed that all the unbaptized were damned. There really is no biblical evidence to support a Limbo of Infants doctrine. The fact that within the Catholic Church itself there are varied positions on this issue demonstrates the weakness of such a position. And most Catholic no longer adhere to this teaching.

The Bible does not teach that salvation comes through baptism or that baptism is necessary for salvation. Baptism is important and it should follow salvation, but it is separate and distinct from salvation, and not required for it. Salvation occurs when a person believes on Christ. It is a work of grace through faith, not a result of some activity.

So what does happen to an infant that dies?

That’s a good and tough question to answer. A concept that is related to this issue is what people sometimes refer to as the “age of accountability.” This term is not found in the Bible, but it is an expression that has been used to refer to the age that a person reaches when he/she is able to understand the Gospel (or whatever revelation God has given to him) and when he is held accountable before God for believing or rejecting the revelation God has given to him.

Obviously an infant would not have reached the “age of accountability.” It is evident also that there are certain people who have such serious mental disabilities that they will never be accountable in this way. It’s impossible to set a single “age of accountability” for every person. Children develop mentally in different ways, and therefore only God knows a person’s “age of accountability.” Our responsibility is to instruct and teach our children from their youngest days, and trust God to work in their hearts.

But the Bible does, however, give us some great hope for believing that when infants die they go immediately and forever to be with the God in Heaven. For example, King David had a child by Bathsheba, which died in infancy. When the child died David's said, “While the child was yet alive, I fasted and wept; for I said, Who can tell whether GOD will be gracious to me, that the child may live? But now he is dead, why should I fast? Can I bring him back again? I shall go to him, but he shall not return to me” (2 Samuel 12:22-23).
The clear sense of this passage is that David believed that he would be reunited with his child in the next life. He knew the baby, having died, could not come back to this life, but he believed that he would go to him. While we can't be dogmatic that such a passage teaches infant salvation, it does seem to point in that direction. Our God is kind and loving as well as just and those who die before the “age of accountability” will be taken care of by the loving and compassionate Savior who died for them.