The aim of this paper is to review concepts, theory, and applications of small sample asymptotic techniques. The striking characteristic of these techniques is that they give uniformly very accurate approximation in the tails of the distribution of a statistics based on n observations even for very small sample sizes. These ideas will be applied to various classes of estimators and tests, including L-estimators, rank procedures, maximum likelihood estimators for general models, and multivariate M-estimators. Other applications to robust statistics, density estimation, and to an efficiency's criterion discussed by Rao will also be discussed.