It finds its origins in Claude Lévi-Strauss's Elementary Structures of Kinship (1949) and is in opposition to the functionalist theory of Radcliffe-Brown.
The incest taboo is thus a negative prescription; without it, nothing would push men to go searching for women outside their inner kinship circle, or vice versa.
Levi-Strauss' model attempted to offer a single explanation for cross-cousin marriage, sister-exchange, dual organisation and rules of exogamy.
When groups exchange women on a regular basis they marry together, with each marriage creating a debtor/creditor relationship which must be balanced through the "repayment" of wives, either directly or in the next generation.
Levi-Strauss proposed that the initial motivation for the exchange of women was the incest taboo, which he deemed to be the beginning and essence of culture, as it was the first rule to check natural impulses; and secondarily the sexual division of labour.
By necessitating wife-exchange arrangements, exogamy therefore promotes inter-group alliances and serves to form structures of social networks.
Levi-Strauss also discovered that a wide range of historically unrelated cultures had the rule that individuals should marry their cross-cousin, meaning children of siblings of the opposite sex - from a male perspective that is either the FZD (father's sister's daughter in kinship abbreviation) or the MBD (mother's brother's daughter in kinship abbreviation).
Generalised exchange is more integrative but contains an implicit hierarchy, for instance amongst the Kachin where wife-givers are superior to wife-takers.
These status inequalities can destabilise the entire system or can at least lead to an accumulation of wives (and in the case of the Kachin also of bridewealth) at one end of the chain.
This "mother's brother" (from the perspective of the wife-seeking son) plays a crucial role in alliance theory, as he is the one who ultimately decides whom his daughter will marry.