How can an allusion be used in modernism?

In terms of literary modernism (early 20th century) writers such as T. S. Eliot, James Joyce, W. H. Auden and Franz Kafka relied heavily on classical allusion in their works.

Joyce's Ulysses is, in a sense, a modern parallel to Homer's Odyssey. Ulysses is the latinised form of Odysseus, Homer's hero and each of the 19 episodes corresponds to particular events and characters in the Odyssey. This was made clear in the Gilbert Schema for Ulysses (written by Joyce for Stuart Gilbert who later published it).

Auden's Musée des Beaux Arts (1937) relates to Pieter Bruegel's work Landscape with The Fall of Icarus, painted around the 1560's, which was derived itself from Ovid's Metamorphoses.

Kafka's The Metamorphosis is also inspired heavily by Ovid's work.

These allusions in Modernist writings are generally an attempt to either bring these works into the modern world, highlighting their timelessness and relevance in the modern world, but also in some cases to try and transcend these classical writings, forming something completely new. This has been criticized in so far as by alluding to classical works in an attempt to transcend them, we are constantly reminded of the original work and thus it is never truly transformed.