When a child is born, the family know that one day he or she will grow up and have it's own independent life, and yet this simple knowledge was not among the Romans.
To them, a baby was a savage individual, needing to learn how to become civilised and that child could only grow into adulthood once it had learnt what it needed to know to become part of the community, part of the working force behind Rome. A baby before becoming a child was considered an infant. The Roman word for infant is infans meaning without speech, just like a wild animal, infants couldn't talk and knew nothing of moral or physical attributes in adult life, but there was a lot more a baby had to go through before it could even reach childhood.

From the very moment a child was brought into the world, it had to pass its first test. It was not immediately part of the Roman family; it had to be accepted before it could take on its name. As soon as the infant was born, the wet-nurse would take it to it's father, and if it was a boy and was accepted, the father would lift the child up into his arms, if it was a girl, the father would just say to feed the child. Babies that were deformed, sickly, and androgynous or had an elephantine head were left to die. Sometimes however, the babies didn't have to be deformed to be abandoned, either because they could not afford to feed the baby or because the father didn't want his already small estate divided between an even greater number of sons. Illegitimate children were not automatically abandoned, they were sometimes adopted and brought up by the mother's father, whose name the child would take, although instead of being called Gaius or Titus, they would be called Spurius, meaning in Latin, "illegitimate".
Abandoned babies were either left out on the streets, suffocated or deprived of any food. Babies left on the streets though, where sometimes picked up by slave traders and given a chance of life. Sometimes the family of the abandoned would track down their child and ask them to rejoin the family and become 'freedmen', but this was not always accepted with enthusiasm. One record of this is of the Head Librarian of the Library of Portia Octavia, Melissus, who was called back by his mother but Melissus, whose status had rose from a low meagre slave refused, saying he didn't want to be a freedman living in poverty.

Babies were weaned by the age of three, and it was only at this stage that the father would take over in the up bringing of the child. Children whose parents were slaves under the roof of their masters were considered to be foster-children of that master and the head of the household would play the part of foster-parent.
Babies were not thought to take on an adult human form and boys were not thought to become men naturally, and reach manhood just on a good diet alone. At birth the baby's body was soft and 'formless', and so had to be hardened and 'moulded'. To mould the baby, it was wrapped in swaddled bands, which were tied around the wrists, elbows, knees, hips, and ankles, particularly tight. The hands were also forced to stay open all the time, and the legs were tied onto splints, while their arms were kept by the sides of the body, tied there, to help keep them perfectly straight. Then they were left 'imprisoned' in their cradles. This routine of shaping the body together went on for two months, after that the bands were loosened, but only a little and the right hand was left free so the child was right-handed.

Roman babies must have detested and dreaded baths, but unfortunately these were to be everyday for the poor infant. They were cold baths because warm baths were considered to have a softening effect on the infant. This was also looked upon as the perfect opportunity for more 'moulding'. This involved the wet-nurse kneading the head of the baby, pummelling it to make it as perfectly round as possible. She would also try to fashion the baby's jaw, nose and it's buttocks.* Pulling the foreskin was also another form of moulding which wet-nurses regularly took as another of their duties. Motherly love was another thing that Roman babies were deprived of, but not because the Roman's didn't love their offspring, it was just thought that to turn the savage uncouth baby into a civilised adult, affection just was not given. Families of nobility even changed their infants wet-nurse three or four times before weaning so no 'attachments' could be formed.
So after the first initial selection process, there was another selection and 'weeding' out process. After all the pummelling, pulling, cold water baths and other rough handling, very few babies actually survived this treatment. It is determined that one out of every three babies survived. One example was of a woman called Cornelia, she had twelve children but only three ever reached adulthood. Religious deities also came into play to help the baby developed from an infans to a Latin-speaking civilised Roman, there were gods for every stage and development of the new born-child.
There were -

Another astonishing fact is that less than fifty percent of the children's population managed to reach it to the age of puberty. This was a very tough process to go through, nature's natural selection by way of illness and then also, the choosing by the fathers and relatives of the infants themselves. Being young and defenceless, illness & afflictions were the bane and dread for any nurse and her charge. One affliction which nurses described as 'emptying the child's flesh' (infantile dysentery?) was considered to be the fault of evil Harpies who would drain the child. There was no cure for this, other than prayers and sacrifices to the various household and infantile deities.
If it was infantile dysentery then it would have been caused by polluted and dirty water, so it may be worth saying that it may have be a popular occurrence between the babies of ancient Rome. Due to ancient tradition, it was thought that a sprig of hawthorn at the opening of any window (these were kept as narrow as possible due to the baby) would help to ward off the evil Harpies. There was even an annual sacrifice to Carna, who was the Goddess of stomach afflictions, to help keep the infants of Rome safe and sound.

*this should not be tried on babies in any way what so ever, it has a deleterious effect!*