The three primary models of fetishism -- anthropological, Marxian, Freudian--all define the fetish as an object endowed with a special force or independent life. Marx called this transference, Freud called it overvaluation. In this sense the fetish is not a representation. It does not refer to something outside itself. 

Anthropological model: Fetishism was a term coined by 15th cent. Portuguese in relation to witchcraft. It was then adopted by Portuguese and later Dutch traders in relation to the cult objects of West Africans. "As an irrational relation to objects, fetishism was not just an abomination in the eyes of the Lord; it was also a damned nuisance to market activity" (Hal Foster, "The Art of Fetishism", in Fetish, Princeton Architecture Journal, 1992, p. 8) This impediment to trade was described by William Pietz as "a perversion of natural processes of economic negotiation and legal contact. Desiring a clean economic transaction, seventeenth century merchants unhappily found themselves entering into social relations and quasi-religious ceremonies that should have been irrelevant to the conduct of trade." -- a process of creative mistranslation at the moment when Western culture confronts the untranslatable other. (Apter, pp 22-23) 

Foster argues that in seventeenth Century Pronk Still-life paintings commodity fetishism partly replace religious fetishism, and that "they employed fetishism as a category to negotiate the different economies of the object that they encountered in the course of market expansion" 

Marxian Model: Commodity fetishism is discussin in Marx, Capital pp 81-83 and in Lukacs, "Reification and the Consciousness of the Proletariat", in History and Class Consciousness 

For Lukacs, "the problem of commodities is the central, structural problem of capitalist society in all its aspects." and "commodity fetishism is a specific problem to our age." Only by understanding the fetish character of commodities, both as an objective form and as a subjective stance can we obtain a clear insight into the ideological problems of capitalism and its downfall. For Lukacs, commodity operates as a "universal structuring principle" 

For Marx, reification occurs "when a definite social relation between men assumes, in their eyes, the fantastic form of a relation between things." Thus the worker comes to define himself as the "owner" of his labor-power --his only possession. "This self-objectification, this transformation of a human function into a commodity reveals in all its starkness the dehumanised and dehumanising function of the commodity relation." 

Freudian Model: "For Freud, fetishism implies both the recognition and the disavowal of reality and the constitution of a substitute." (Sarah Kofman)

The fetish is a substitute for the (maternal) In the course of the child's "infantile sexual research" (he) discovers that his mother does not have a penis and thinks it to be castrated. The fetish is nothing but "the substitute for the woman's (the mother's) penis that the little boy once believed in and -- for reasons familiar to us -- does not want to give up." The fetish (such as the foot fetish) screens out this castration and so blocks its threat. It is a structure of ambivalence, in Freud's words, it is a "memorial to castration" which allows the woman (mother) to be seen as both whole and castrated. "Fetishism" in On Sexuality. "The fetish is simultaneously the presence of that nothingness that is the maternal penis and the sign of its absence." (Agamben)For Agamben the fetish is an emblem of secret fear and desire that enables the appropriation of unconscious content without bringing it to consciousness. 

Freud's fetishist seems to operate entirely in the realm of the simulacrum, generating a copy or surrogate phallus for an original that was never there in the first place. (Apter. p.28) According to Emily Apter, this attitude towards the object-simulacrum expresses an uneasy mixture of credulity and disbelief. For a very different account of neurological bases of fetishism, see V.S. Ramachandran's account of the neurological links between foot and genital. (see brain)

Jeff Kipnis attributes to "strong discourse" the ability to discern between the normal and the pathological. This juridical concept can then claim that a real shoe properly exemplifies shoeness, while it is a perversity for an other meaning, such as the mother's phallus, to slip into it. (p.163) Kipnis argues that objects have an unbounded capacity to exceed the specfic meanings that discourse tries to assign to them. Is this another form of fetishism? a fetishism of disavowal?

Deleuze and Guattari criticize psychology for not seeing the " becoming-animal, that is affect in itself, the drive in person, and represents nothing." They describe children as continually undergoing becomings of this kind, and find these "unnatural participations" in fetishism and particularly masochism. (1000 Plateaux, p. 259)

The power of the fetish can also be seen in the confusion of animate and inanimate of the Golem or cyborg.