In ancient Rome, adoption (adoptio) meant taking a son or daughter from another family under paternal authority. Adoption was carried out in the presence of a praetor or governor. The adoptive consent was not required. The most common reason for the adoption was the need to maintain the continuity of the family.
In ancient Rome, boys were most often adopted, especially in the higher ranks, e.g. senators. This was mainly due to the need to keep the heir and the fact that it cost the father much more to get his daughter married (a substantial dowry) than the other way around. Moreover, the adoption allowed for political alliances to be made between the families, and the sons ensured that the family could grow in power on the Roman political scene.
Sometimes there were cases where many male descendants were born in the house of a high-ranking Roman family and it was decided to give the sons to another family. A good example is the wealthy Lucius Aemilius Paullus of Macedon, who did not hesitate to give his two sons up for adoption: one son was given to Scipio Africanus the Younger, and the other lineage Fabia.
The custom of adoption prevailed at the very highest levels of power in the Roman Empire. Among others, the Antonine dynasty became famous for the fact that subsequent emperors (Trajan, Hadrian, Antoninus Pius, Marcus Aurelius) were not born sons, but only adopted ones.
The right to put a child up for adoption lay in the hands of paterfamilias. Usually, it was the oldest and healthy member of the family. If a child moved from a commoner house to a patrician house, it automatically became a patrician; and vice versa. Moreover, adopted children had the same rights in a Roman family as all other children.