The article considers the main aspects of Joyce’s indebtedness to the Homeric source text, provides an essential survey of the most influential critical evaluations of Joyce’s use of Homeric and Classic Greek references (Stanford, Ellmann, Schork, Arkins), focusses on questions of appropriation in Anglophone Modernism (referring to Eliot’s “mythical method” and earlier poetic models such as Tennyson’s) and finally dwells on the “polytropic” nature of Leopold Bloom as the truest and most suggestive Odyssean quality, and the most persuasive element of the actualization of myth into the modernist narrative of Ulysses.