A popular method for selling excess inventory over the Internet is via a Name-Your-Own Price auction, where the bidder bids on an item and the seller immediately decides on whether or not to accept the bid. The analytical modeling of such auctions is still in its infancy. A number of papers have appeared over the last few years making various assumptions about buyers and sellers. The intent of this article is to carefully delineate the various assumptions and modeling approaches and, consequently, suggest avenues for further research.