When some population values are completely from observation, the distribution from which the observations came is said to be truncated. Estimation of the parameters from truncated distributions has been an open field for research. This thesis examines the developments which have taken place in this area, giving the major writers and the methods used by them to obtain estimators. A. C. Cohen is responsible for much work involving the maximum likelihood procedure. Using the method of moments and several methods which they have developed, Rider, Plackett, Samford, Moore, Des Raj, and Halperin have made significant contributions. The Poisson, Normal, Binomial, Negative Binomial, and Gamma distributions are included in the investigation and along with the estimators, in some cases, asymptotic variances are given. Though much work has been done, there are many things left to be investigated. Only a small number of distributions have been dealt with, with all multivariate distributions other than the normal lacking any investigation. It is not known how the estimators are affected by small sample sizes, and with the aid of the computer variances can be examined. A new problem arises when the points of truncation are not clearly defined and complicated equations often make estimators difficult to fine. / M.S.