Auctions usually involve the sale of many homogeneous or heterogeneous objects. Spectrum, treasury, and electricity auctions are examples. This kind of auctions is so-called multi-unit auctions. In order to know the research history and the newest research trends for the study on multi-unit auctions, this paper presents widespread theoretical and applications problems of multi-unit auctions. The multi-unit auction models are divided into two kinds (i.e. sequential auction and simultaneous auction). Assumptions, main ideas, and conclusions of literature related to these two kinds of models are reviewed and commented.