From Abrams and Harpham, A Glossary of Literary Terms (10th ed.), 146:

Gender criticism, like the gender studies of which it is a part, is based on the premise that, while sex (a person’s identification as a male or a female) is based on anatomy, gender (masculinity or femininity in personality traits and behavior) can be largely independent of anatomy, and is a social construction that is diverse, variable, and dependent on historical circumstances. Gender criticism analyzes differing conceptions of gender and their role in the writing, reception, subject matter, and evaluation of literary works.

From Gayle Rubin, “The Traffic in Women: Notes on the ‘Political Economy’ of Sex” (1975):

[Freud and Levi-Strauss] provide conceptual tools with which one can build descriptions of the part of social life which is the locus of the oppression of women, of sexual minorities, and of certain aspects of human personality within individuals. I call that part of social life the "sex/gender system," for lack of a more elegant term. As a preliminary definition, a "sex/gender system" is the set of arrangements by which a society transforms biological sexuality into products of human activity, and in which these transformed sexual needs are satisfied. (159)

The needs of sexuality and procreation must be satisfied as much as the need to eat, and one of the most obvious deductions which can be made from the data of anthropology is that these needs are hardly ever satisfied in any "natural" form, any more than are the needs for food. Hunger is hunger, but what counts as food is culturally determined and obtained. Every society has some form of organized economic activity. Sex is sex, but what counts as sex is equally culturally determined and obtained. Ever society also has a sex/gender system --a set of arrangements by which the biological raw material of human sex and procreation is shaped by human, social intervention and satisfied in a conventional manner, no matter how bizarre some of the conventions may be. (165)

Any society will have some system of "political economy." Such a system may be egalitarian or socialist. It may be class stratified, in which case the oppressed class may consist of serfs, peasants, or slaves. The oppressed class may consist of wage laborers, in which case the system is properly labeled "capitalist." The power of the term lies in its implication that, in fact, there are alternatives to capitalism.

Similarly, any society will have some systematic ways to deal with sex, gender, and babies. Such a system may be sexually egalitarian, at least in theory, or it may be "gender stratified," as seems to be the case for most or all of the known examples, But it is important--even in the face of a depressing history—to maintain a distinction between the human capacity and necessity to create a sexual world, and the empirically oppressive ways in which sexual worlds have been organized. Patriarchy subsumes both meanings into the same term. Sex/gender system, on the other hand, is a neutral term which refers to the domain and indicates that oppression is not inevitable in that domain, but is the product of the specific social relations which organize it. (167-68)

Human sexual life will always be subject to convention and human intervention. It will never be completely "natural," if only because our species is social, cultural, and articulate. The wild profusion of infantile sexuality will always be tamed. The confrontation between immature and helpless infants and the developed social life of their elders will probably always leave some residue of disturbance. But the mechanisms and aims of this process need not be largely independent of conscious choice. Cultural evolution provides us with the opportunity to seize control of the means of sexuality, reproduction, and socialization, and to make conscious decisions to liberate human sexual life from the archaic relationships which deform it. Ultimately, a thoroughgoing feminist revolution would liberate more than women; it would liberate forms of sexual expression, and it would liberate human personality from the straightjacket of gender. (199-200)

Finally, the exegesis of Levi-Strauss and Freud suggests a certain vision of feminist politics and the feminist utopia. It suggests that we should not aim for the elimination of men but for the elimination of the social system which create sexism and gender. I personally find a version of an Amazon matriarchate, in which men are reduced to servitude or oblivion (depending on the possibilities for parthenogenetic reproduction), distasteful and inadequate. Such a vision maintains gender and the division of the sexes. It is a vision which simply inverts the arguments of those who base their case for inevitable male dominance on ineradicable and significant biological differences between the sexes. But we are not only oppressed as women, we are oppressed by having to be women, or men as the case may be. I personally feel that the feminist movement must dream of even more than the elimination of the oppression of women. It must dream of the elimination of obligatory sexualities and sex roles. The dream I find most compelling is one of an androgynous and genderless (though not sexless) society, in which one's sexual anatomy is irrelevant to who one is, what one does, and with whom one makes love. (204)

Cp. Wittig, “One Is Not Born a Woman”:

Matriarchy is no less heterosexual than patriarchy: it is only the sex of the oppressor that changes. Furthermore, not only is this conception still imprisoned in the categories of sex (woman and man), but it holds onto the idea that the capacity to give birth (biology) is what defines a woman. (1907)