The approval of the revised rule on the acceptance of emergency core cooling system performance in 1988 triggered a significant interest in the development of codes and methodologies for uncertainty evaluation of best-estimate loss-of-coolant accident (LOCA) analyses. The code scaling, applicability, and uncertainty evaluation method was developed and demonstrated for a large-break LOCA in a pressurized water reactor. Later, several new best-estimate plus uncertainty methods (BEPUs) were developed around the world. The purpose of this paper is to identify and compare the statistical approaches of BEPU methods and present their importance for licensing applications in nuclear power plants. The study showed that the uncertainty analysis with random sampling of input parameters, using the nonparametric statistical tolerance limits for estimating uncertainty of output parameters, is the commonly accepted approach today. The existing BEPU methods seem mature enough, while the future research may be focused on the codes with internal assessment of uncertainty.