One of the foundational works in the anthropological study of kinship was Morgan's Systems of Consanguinity and Affinity of the Human Family (1871). As is the case with other social sciences, Anthropology and kinship studies emerged at a time when the understanding of the Human species' comparative place in the world was somewhat different from today's. Evidence that life in stable social groups is not just a feature of humans, but also of many other primates, was yet to emerge and society was considered to be a uniquely human affair. As a result, early kinship theorists saw an apparent need to explain not only the details of how human social groups are constructed, their patterns, meanings and obligations, but also why they are constructed at all. The why explanations thus typically presented the fact of life in social groups (which appeared to be unique to humans) as being largely a result of human ideas and values.
Morgan's explanation for why humans live in groups was largely based on the notion that all humans have an inherent natural valuation of genealogical ties (an unexamined assumption that would remain at the heart of kinship studies for another century, see below), and therefore also an inherent desire to construct social groups around these ties. Even so, Morgan found that members of a society who are not close genealogical relatives may nevertheless use what he called kinship terms (which he considered to be originally based on genealogical ties). This fact was already evident in his use of the term affinity within his concept of the system of kinship. The most lasting of Morgan's contributions was his discovery of the difference between descriptive and classificatory kinship terms, which situated broad kinship classes on the basis of imputing abstract social patterns of relationships having little or no overall relation to genetic closeness but instead cognition about kinship, social distinctions as they affect linguistic usages in kinship terminology, and strongly relate, if only by approximation, to patterns of marriage.
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A more flexible view of kinship was formulated in British social anthropology. Among the attempts to break out of universalizing assumptions and theories about kinship, Radcliffe-Brown (1922, The Andaman Islands; 1930, The social organization of Australian tribes) was the first to assert that kinship relations are best thought of as concrete networks of relationships among individuals. He then described these relationships, however, as typified by interlocking interpersonal roles. Malinowski (1922, Argonauts of the Western Pacific) described patterns of events with concrete individuals as participants stressing the relative stability of institutions and communities, but without insisting on abstract systems or models of kinship. Gluckman (1955, The judicial process among the Barotse of N…

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Like Schneider, other anthropologists of kinship have largely rejected sociobiological accounts of human social patterns as being both reductionistic and also empirically incompatible with ethnographic data on human kinship. Notably, Marshall Sahlins strongly critiqued the sociobiological approach through reviews of ethnographies in his 1976 The Use and Abuse of Biology noting that for humans "the categories of 'near' and 'distant' [kin] vary independently of consanguinal distance and that these categories organize actual social practice" (p. 112).

Independently from anthropology, biologists studying organisms' social behaviours and relationships have been interested to understand under what conditions significant social behaviors can evolve to become a typical feature of a species (see inclusive fitness theory). Because complex social relationships and cohesive social groups are common not only to humans, but also to most primates, biologists maintain that these biological theories of sociality should in principle be generally applicable. The more challenging question arises as to how such ideas can be applied to the human species whilst fully taking account of the extensive ethnographic evidence that has emerged from anthropological research on kinship patterns.

Early developments of biological inclusive fitness theory and the derivative field of Sociobiology, encouraged some sociobiologists and evolutionary psychologists to approach human kinship with the assumption that inclusive fitness theory predicts that kinship relations in humans are indeed expected to depend on genetic relatedness, which they readily connected with the genealogy approach of early anthropologists such as Morgan (see above sections). However, this is the position that Schneider, Sahlins and other anthropologists explicitly reject.
In agreement with Schneider, Holland argued that an accurate account of biological theory and evidence supports the view that social bonds (and kinship) are indeed mediated by a shared social environment and processes of frequent interaction, care and nurture, rather than by genealogical relationships per se (even if genealogical relationships frequently correlate with such processes). In his 2012 book Social bonding and nurture kinship Holland argues that sociobiologists and later evolutionary psychologists misrepresent biological theory, mistakenly believing that inclusive fitness theory predicts that genetic relatedness per se is the condition that mediates social bonding and social cooperation in organisms. Holland points out that the biological theory (see inclusive fitness) only specifies that a statistical relationship between social behaviors and genealogical relatedness is a criterion for the evolution of social behaviors. The theory's originator, W. D. Hamilton considered that organisms' social behaviours were likely to be mediated by general conditions that typically correlate with genetic relatedness, but are not likely to be mediated by genetic relatedness per se (see Human inclusive fitness and Kin recognition). Holland reviews fieldwork from social mammals and primates to show that social bonding and cooperation in these species is indeed mediated through processes of shared living context, familiarity and attachments, not by genetic relatedness per se. Holland thus argues that both the biological theory and the biological evidence is nondeterministic and nonreductive, and that biology as a theoretical and empirical endeavor (as opposed to 'biology' as a cultural-symbolic nexus as outlined in Schneider's 1968 book) actually supports the nu…

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As social and biological concepts of parenthood are not necessarily coterminous, the terms "pater" and "genitor" have been used in anthropology to distinguish between the man who is socially recognised as father (pater) and the man who is believed to be the physiological parent (genitor); similarly the terms "mater" and "genitrix" have been used to distinguish between the woman socially recognised as mother (mater) and the woman believed to be the physiological parent (genitrix). Such a distinction is useful when the individual who is considered the legal parent of the child is not the individual who is believed to be the child's biological parent. For example, in his ethnography of the Nuer, Evans-Pritchard notes that if a widow, following the death of her husband, chooses to live with a lover outside of her deceased husband's kin group, that lover is only considered genitor of any subsequent children the widow has, and her deceased husband continues to be considered the pater. As a result, the lover has no legal control over the children, who may be taken away from him by the kin of the pater when they choose. The terms "pater" and "genitor" have also been used to help describe the relationship between children and their parents in the context of divorce in Britain. Following the divorce and remarriage of their parents, children find themselves using the term "mother" or "father" in relation to more than one individual, and the pater or mater who is legally responsible for the child's care, and whose family name the child uses, may not be the genitor or genitrix of the child, with whom a separate parent-child relationship may be maintained through arrangements such as visitation rights or joint custody.

It is important to note that the terms "genitor" or "genetrix" do not necessarily imply actual biological relationships based on consanguinity, but rather refer to the socially held belief that the individual is physically related to the child, derived from culturally held ideas about how biology works. So, for example, the Ifugao may believe that an illegitimate child might have more than one physical father, and so nominate more than one genitor. J.A. Barnes therefore argued that it was necessary to make a further distinction between genitor and genitrix (the supposed biological mother and father of the child), and the actual genetic father and mother of the child making them share their genes or genetics .
The study of kinship may be abstracted to binary relations between people. For example, if x is the parent of y, the relation may be symbolized as xPy. The converse relation, that y is the child of x, is written yP x. Suppose that z is another child of x: zP x. Then y is a sibling of z as they share the parent x: zP xPy → zP Py. Here the relation of siblings is expressed as the composition P P of the parent relation with its inverse.

The relation of grandparent is the composition of the parent relation with itself: G = PP. An uncle or aunt is the sibling of a parent, (P P)P, which can also be interpreted as the child of a grandparent, P (PP). Suppose x is the grandparent of y: xGy. Then y and z are cousins if yG xGz.

The symbols applied here to express kinship are used more generally in algebraic logic to develop a calculus of relations with sets other than human beings.