This paper briefly reviews the literature on the topics of noise traders in the financial market. We cover the no-trade theorem under complete and competitive markets in the 1980s, the noise trader approach to finance in the 1990s, and recent studies from several approaches related to noise traders, such as heterogeneous agent models, investor sentiment, retail investors, experimental analysis, and extrapolation. Understanding and tackling the issues resulted from noise traders would be essential for us to realize how financial and economic markets work.