Studies using drought index to examine return levels of drought can be classified into two approaches: univariate frequency analysis using annual series extracted from drought index time series and multivariate frequency analysis that simultaneously reflects various characteristics of drought. In the case of drought analysis, it is important to properly consider the duration, so, in this study, univariate frequency analysis is performed using the partial duration series. In addition, a bivariate frequency analysis is performed using a relatively simple bivariate exponential distribution to give a more realistic return level to major drought events in the past while reflecting the correlation between drought severities and durations. The drought severity–duration–frequency curves using each of the two frequency analyses are derived, and these curves are used to examine how the drought phenomenon currently in progress is evolving. From this, the advantages and disadvantages of the two approaches, as well as the points to be aware of in application, are discussed. Finally, using the two approaches to the proposed drought frequency analysis, the behavior of Korea’s future extreme droughts is investigated under the conditions of various future climate change scenarios.