According to Catholicism what happens to young children who die before being baptized? John 3:5 is as follows:


  Jesus answered, “Very truly I tell you, no one can enter the kingdom
  of God unless they are born of water and the Spirit.


In the light of that, what happens to those who die before being baptized ? For example, what happens to a baby who dies in the womb of his/her mother ? Or a 5 year old child ? Basically, someone who is not mature enough to reason.
Thomas Aquinas hypothesised that a merciful God would not consign innocent babies who died without being purged of Original Sin through baptism, to hell. Aquinas said these innocents must dwell in limbo, a place between heaven and hell, alongside virtuous but unbaptised pagans such as Plato and Moses, born before Jesus had come to explain things. Thus limbo became a Catholic tradition and had Church approval as such. 

Now, the International Theological Commission says:


  It is clear that the traditional teaching on this topic has concentrated on the theory of limbo, understood as a state which includes the souls of infants who die subject to original sin and without baptism, and who, therefore, neither merit the beatific vision, nor yet are subjected to any punishment, because they are not guilty of any personal sin. This theory, elaborated by theologians beginning in the Middle Ages, never entered into the dogmatic definitions of the Magisterium, even if that same Magisterium did at times mention the theory in its ordinary teaching up until the Second Vatican Council. It remains therefore a possible theological hypothesis. However, in the Catechism of the Catholic Church (1992), the theory of limbo is not mentioned.


So, if you were taught the catechism before 1992, or enquired more fully before Vatican II, you could have been told about limbo and assured that it is real, but you would not easily find such a teaching now. Nevertheless limbo is undoubtedly a strong Catholic tradition, has been taught by the Church and had Church approval, even though it never entered into the dogmatic definitions of the Magisterium.

Since Vatican II, the Catholic Church has begun to move away from its former teachings about limbo and treat it as no more than a hypothesis, and there have been suggestions that the hypothesis will eventually be abandoned. Recent Catholic theological speculation tends to stress the hope, though not the certainty, that unbaptised infants may attain heaven instead of the supposed state of limbo.