Anthropologists found, kinship played a huge role in institutions like religion justice economic and political system. how rights duties status and property are transmitted from one generation to the next. So they started to you understand kinship and its origin, which resulted in 2 famous theories.

Descent theory

Also called linear theory. Became prominent with the the publication of The Nuer 1940.
Kinship is determined by decent which is traced from the ancestor and it can be e unilineal or multi lineal. it can be traced from father's side on mother side and the person becomes kin to others and also inherits status property rules rights and duties based on this decent.
Criticism.

Ev Pritchard argued that individuals could not always identify with the lineage they belong to.
in matrilineal society even though kinship is traced by decent from the mother the institution of political power and authority was with men. Also men did not pass the authority to their sons.
It minimise the importance of marriage in the structuring of kinship. Which was later pointed out by Levi Strauss and his alliance theory.

Alliance theory

Levi Strauss in his book elementary structures of kinship gave this theory. He argued that kinship originated when humans transition from nature to culture. Humans viewed each other as us and them and in order to survive the started building alliances by exchanging women which he considers the supreme gift.
Since reciprocity is fundamental form of exchange among humans, the woman taking group reciprocated by offering women in same generation or the next. Therefore alliance was created among two groups and fundamental structures or atoms of kinship were formed in form of husband wife relations father and son, II relationship of son with mother brother and so on.
With time two groups cannot sustain reciprocity for long due to various factors therefore exchange of women started to take place in a more general way among society. Therefore more complex forms of kinship emerged. Finally this kinship becomes the basis for linking and organising various parts of Life light politics economy religion.
It helped understand the the tribal groups of New Guinea Indonesia and South America where descent model was not applicable.
Criticism

Both theories were criticized for ignoring experiential and emotional sides of kinship and variations of gender and social actors. They viewed kinship in normative terms only.
Feminist anthropologists criticised levi-strauss for objectifying women as goods of exchange.

But today both of these theories are obsolete.

Descent and alliance theory 1-2