The outlier detection is an important task of data mining and knowledge discovery in database. Its necessities in astronomy are reviewed with the definitions, characteristics, forming reasons and causing effects of outliers being simply introduced. The methodologies to detect univariate outliers and multivariate outliers are summarized, and compared with other clustering algorithms. Since each kind of approach has its own pros and cons, astronomers should reasonably choose methodologies to detect outliers according to the characteristics of astronomical data, so that some unusual, rare or even new astronomical objects and phenomena could be found.