In the present book, Chapter I gives the introduction about the concept of outliers along with the statistical inference in linear regression model. The various test statistics for detecting outliers such as Maximum Normed Residual, Extreme Studentized Deviation, Studentized Range, Kurtosis, R-Statistic, Maximum Eigen differences Least Medium Squares (LMS) estimator, Mahalanobis Distance, Cooks Distance, DFFITS, DF BETAS, COVRATIO, Scale ratio, Gap Test Statistic and 2-sigma Region have been described in Chapter II. Different test procedures to detect the outliers have been reviewed in brief in Chapter III. In Chapter IV some new tests for detecting outliers have been suggested based on different types of residuals and dummy variables.The summary and conclusions along with plan for the future research have been in Chapter V. Several research articles and related books are presented under BIBLIOGRAPHY.