It is well known that at the beginning of the 1960s there was a rigorous debate between two leading intellectuals in France, namely Lévi-Strauss the structural anthropologist and Sartre the existential phenomenologist turned Marxist. While Sartre criticized Lévi-Strauss' structural method of neglecting the entire historical dimension of human culture, the father of structural anthropology retorted that Sartre's philosophy of consciousness, like all philosophy of subject, is unable to account for the structurally unconscious dimension of human and cultural life. The present chapter does not aim at a historical reconstruction of this famous debate. It aims rather at re-articulating the philosophical issues at stake. We will focus on the theoretical question raised by Lévi-Strauss, namely the question of the distinction between nature and culture, and examine in what way his structural approach constitutes a severe challenge to phenomenology as a contemporary form of philosophy of subject. We will then explore in what way Merleau-Ponty's late ontology, while questioning also the nature-culture distinction by returning to the pre-reflective and pre-objective order of brute being and savage spirit, is a mode of genetic phenomenology which shares some important insights of Levi-Strauss' structural anthropology and hence can accommodate the challenge from the latter. After this anthropological-ontological confrontation, we will try to draw its implications for intercultural understanding from a phenomenological perspective on the following four aspects: (1) psychoanalysis as myth and the primitive side of Western civilization; (2) distance and other cultures as co-constitutive of total Being and total truth; (3) broadening of Reason by lateral universals; (4) Indian and Chinese Philosophies as other relationships to Being that the West has not opted for.