The Weibull distribution is widely adopted as a lifetime distribution. One of the characteristics the Weibull distribution possesses is that its cumulative distribution function can be expressed by closed form. Parameter estimation for the Weibull distribution has been discussed by many authors. Various methods have been proposed for constructing confidence intervals and joint confidence regions for the parameters of the Weibull distribution based on censored data. This paper discusses those methods that deal with exact confidence intervals or exact joint confidence regions for the parameters. One of the applications of the joint confidence regions of the parameters is to find confidence bounds for the functions of the parameters. In this paper, confidence bounds for the mean lifetime and reliability function for the Weibull distributions are discussed. Some unresolved problems for the exact confidences and joint confidence regions are mentioned in the discussion section.