One can discern basically four types of approaches to the Apocalypse in the 20th century. The first method is called the History of Religions method. This grows out of an important type of biblical criticism that developed in Germany at the end of the 19th century, the History of Religions school or "Religionsgeschichtelicheschule" (which I abbreviate RGS). As you may know, in the 19th century there was an increasing tendency to place NT texts in their historical context in terms of the history and development of early Christianity rather than in the purely theological context of the development of Christian doctrine, dogma, and theology. There was also parallel developments in the study of folklore and ethnology (think of the brothers Grimm) and the mythologies and cultures that lay behind classical texts such as Homer's Odyssey. The History of Religions school or RGS at Gottingen pushed the study of the relation of NT and early Christianity to its mythological parallels and antecedents in Ancient Near Eastern culture and religion. For the RGS method, explaining where religions ideas and images came from was most important.
One important RGS study of Revelation by Hermann Gunkel showed that there were elements in the text, in Revelation 12 in particular, that could not be explained purely in terms of biblical or Jewish and Christian motifs. He thought the passage contained ideas and images that could be traced back to the ancient Babylonian creation myth, the Enuma Elish. Gunkel then placed or "explained" (for himself, at least) the images in Revelation 12 in reference to a more ancient religious tradition. As you can imagine, the imagery of Revelation provides a host of opportunities for this sort of comparative work.
The second prominent interpretive strategy of the twentieth century is more explicty theological. Theological intepretations of Revelation stand in the mainline of the biblical interpretive tradition as ideas and images are explained by reference to the development of Jewish and Christian theology. But as you may know, Revelation has not been a favorite text of most theologians, who tend to prefer Paul and the Gospel of John to the Apocalypse's bizarre images and harsh theology. Rudolf Bultmann was merely following Luther when he dismissed Revelation as a Jewish text with a thin veneer of Christianity added to it (we could of course discuss why Bultmann thought it was bad to be Jewish!). The basic question in theological approaches is how the text fits with Christian theology; the approach is often orthodox or pietistic.
A third method of approach is social-historical and sociological. Sociological studies of Revelation and early Christianity have borrowed heavily from anthropological studies of Cargo Cults in the Pacific islands or other millenarian movements. It is interesting that such anthropological studies have been influenced by the book of Revelation; note the title of Kenelm Burridge's New Heaven, New Earth. Sociological researchers take these studies of millenarian or messianic groups in the twentieth century and apply the data to reconstructions of the early Christian communities. These studies raise the issue of commensurability, or whether modern scientific methods are applicable to other cultures or to situations with much less data. Scholars debate anthropological methodological issues such as functionalism as opposed to symbolic culture interpretation along the lines of Clifford Geertz. The basic question in sociological approaches is explaining how the text functioned within its community, social setting, or culture. This has been my own line of research, with an ideological-rhetorical bent. My particular interests are the constructions and expressions of power and dominance in the text and the late first or early second century Christian communities in Asia Minor, the Roman province where the Seven Cities of the Apocalypse were located.
A fourth method of interpretation of the book of Revelation is literary interpretation. This group has seen a number of interesting works, from D. H. Lawrence's Apocalypse to Austin Farrer's Jungian commentary to Frank Kermode's The Sense of an Ending to recent post-structural readings by Harold Bloom and Tina Pippin. Pippin and post-modern other scholars such as Catherine Keller and Stephen D. Moore have also raised ideological questions in their critical studies of the text in contempory contexts. Literary interpretations ask how the text functions or reads as literature. As you can imagine, the number of approaches are as vast as the "-isms" of literary criticism and the scholars. A text such as Revelation offers limitless interpretive possibilities for literary or mythological studies; it is, as Umberto Eco would say, an "open work."
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