For the first time, the beta Burr III distribution is introduced as an important model for problems in several areas such as actuarial sciences, meteorology, economics, finance, environmental studies, survival analysis and reliability. The new distribution can be expressed as a linear combination of Burr III distributions and then it has tractable properties for the moments, generating and quantile functions, mean deviations, reliability and entropies. The density of its order statistics can be given in terms of an infinite linear combination of Burr III densities. The beta Burr III model is modified for the possibility of long-term survivors. We define a log-beta Burr III regression model to analyze censored data. The estimation of parameters is approached by maximum likelihood and the observed information matrix is derived. The proposed models are applied to three real data sets.