Undoubtedly, it is important to model the average and extreme phenomena in earth sciences disciplines such as hydrology under uncertain and changing climate conditions. The issues become more important when we deal with reservoir management, flood forecasting and irrigation. In this paper, we model the average and extreme river flow in the Indus River at the Upper Indus Basin. For modelling average river flow, we utilised the popular classes of time series models including the autoregressive integrated moving average and autoregressive conditional heteroscedasticity models. For modelling the extremes, preference is given to probability distributions dealing with extremes in the tails. Starting with different models and distributions we finally choose the one which performs best among the competing models and distributions, respectively. Finally, when modelling extremes we noted that different probability distributions may be used for the same data, depending on whether interest is in lower or higher order moments.