Extreme climate events and their impacts are currently arising as a critical feature of climate change. Paleoclimate studies are essential for understanding global environmental change and predicting extreme’s trends as the paleo-studies determine the factors that caused changes in the climate. Many studies have suggested that the mid-Pliocene and last interglacial (LIG) can be potentially used as an analogue for the future climates, but the extreme climate events are often missing in these studies. This thesis aims to show whether the LIG and mid-Pliocene are considered as analogues for the future of two extreme climate indices, including summer days index and heavy precipitation index. The MPI-ESM and COSMOS are employed to simulate the LIG, mid-Pliocene, pre-industrial, and future climates. First, the anomalies of temperature, precipitation, and selected indices are plotted for the simulations with respect to PI. In general, the summer days and heavy precipitation patterns are similar to the temperature and precipitation patterns, respectively. The probability density functions of climate variables and extreme indices in the centre of North America and Africa, the south of Africa, and Malaysia, clearly show that the increases in the average temperature and precipitation result in a growth in the corresponding extreme index. Comparing the anomaly plots for different simulations, the LIG can be only considered as analogue for future of summer days index in the northern-hemisphere regions such as the centre of North America. The mid-Pliocene not only is a good analogue for the summer days at the global scale but also can be used regionally for the prediction of heavy precipitation events. Due to the different characteristics of models employed in this project, there are some discrepancies in the results of similar simulations produced by MPI-ESM and COSMOS.