Much of knowledge on future climate change depends on projections from the simulation codes with global circulation models (GCMs) and regional climate models (RCMs). But even state-of-art simulation codes still have a rather coarse resolution and are substantially biased compared to real-world climate. In an attempt to remove systematic biases between simulation model output and real observations, a variety of statistical bias correction (BC) methods has been developed. The methods are classified to univariate and multivariate ones. This study reviews these techniques with more emphasis on recently advanced multivariate methods. These includes delta change approach, quantile mapping, quantile delta mapping, empirical copula bias correction, multivariate quantile delta mapping and multivariate stochastic BC with optimal transport function. An application of multivariate BC method to annual daily extreme rainfall in Korea peninsula is presented. We applied an ensemble prediction with generalized extreme value distribution (GEVD) to the data obtained as simulated by the coupled model intercomparison project phase six (CMIP6) models. Simulation data under three RCP (Representative Concentration Pathway) scenarios, namely RCP 2.6, RCP 4.5 and RCP 8.5, are employed. The 20-year and 50-year return levels and return periods relative to the reference years (1973-2014) are estimated for two future periods, namely period 1 (2021-2050) and period 2 (2061-2099).