The first thing that should be noted, prior to stepping through the major influences and schools within preterist thought is: Every scholar (those who have done the requisite post-doctoral level research, are published and reviewed by their peers, and are thus respected by their contemporaries as a scholar) is a preterist to some degree.
And what do I mean by preterist? One that calculates that a prophecy (in part or full) that was forward looking from the perspective (or conveyed context) of an author in the New Testament has been fulfilled since that writing/recording/context. A most obvious example that is universally acknowledged by scholars is that Jesus predicted a cataclysm upon the (then standing) temple in Jerusalem. The temple was in fact largely destroyed in a Roman siege in AD 70. (There is a brand of eschatology that looks forward to a like destruction in the future, but this a small contingent in the world of scholarship, and even they acknowledge a 1st century fulfillment, if partial as they look to the penultimate.)
So in this sense, as all are preterists, the word comes to bear no meaning. My use of the word 'preterist' here then applies to those who see more than the consensus view/groundwork regarding the prophecies of the New Testament. In the next segment, I hope to focus on the differences within preterism concerning expectations and interpretations of (expected and past) fulfillment of the Olivet discourse(s) and its relation to John's Apocalypse and Pauline expectation.