From Planck's Constant:
Adoption under Islamic law is different than commonly practiced in other cultures. The term that Muslims use for their version of adoption is called kafala, meaning "to feed," which is more descriptive of a foster parent than an adoptive parent.
One may wonder why the Quran forbids Muslim parents to treat their adopted children the same as their biological children. For example, adopted children do not inherit from their adoptive parents and adopted children are not maharim (1)to their adoptive family, that is, they are not blood relatives and so a Muslim man may legally have sex with his adopted daughter (or with his adopted son's wife).