The issue of child custody has been debated among Muslim faqihs and jurists for a long period of time. In this paper, the author argues that child custody is a type of guardianship that God Almighty has conferred upon parents, fathers and then mothers. It is not a "right", which can be waived, but it is an "obligation" that parents must fulfill. There are, however, specific parental duties that can be waived, as mothers can refrain from breastfeeding their children. Also, under certain circumstance, the Shari'a allows the abrogation of custodianship duties. It has been proved that natural parents, and not the Islamic state or society as a whole, are responsible for the custody of their illegitimate children. Such children ought to be treated as legitimate children, thought they do not inherit any property from their parents.