This paper is to survey the major results of the game-theoretic models and recent research directions of the literature on auctions and competitive biddings. This paper classifies the auctions and competitive biddings into the following four major types:(i) English auction, (ii) Dutch auction, (iii) the first-price sealed-bid auction, (iv) the second-price sealed-bid auction. In order to survey the major ideas related to auctions and competitive biddings, we use two representative theoretical models developed under the game-theoretic framework : (i) the independent private value model are summarized as follows ; (1) The Dutch auction and the first-price auction are strategically equivalent, and so are the English auction and the second-price auction. (2) At the symmetric equilibria, the expected selling price is the same for all four types of auction. Meanwhile, the major results of the general model are as follows ; (1) When bidders are uncertain about their value extimate, the English and second-price auctions are not equivalent, but the dutch and the first-price auctions are still strategically equivalent. (2) The English auction generates the higher expected prices than the second-price auction. Also, when bidders are risk-neutral, the second-price auction generated higher average prices than the Dutch and the first-price auctions.