Abstract: The East Asian Summer Monsoon (EASM), which has profound societal and economic impacts in China, has exhibited multiple time-scale variabilities. Climate models play an irreplaceable role in understanding the past changes and predicting/projecting the future changes in the EASM. However, current state of the climate models still shows evident biases in the simulation of EASM. This kind of model deficiency has limited our understanding of the mechanisms responsible for the EASM variability based on numerical model experiments and reduced the reliability of long-term climate change projection. This paper provides a synthesis review on our progresses in climate modeling study with a focus on the EASM. The achievements made in the last 5 years are summarized along with an extension to earlier studies in case of needing. The observational metrics used to gauge model performances include the climatology, diurnal cycle, interannual variability, interdecadal variability, and long-term climate change and climate projection. The following processes that are crucial to a successful modeling of monsoon mean state, variability and changes are reviewed, which include the effects of model resolution and model topography, climate effects of moist convection and cloud-radiation, monsoon-related tropical air-sea interactions, impacts of internal variability modes such as the Pacific Decadal Oscillation on the inter-decadal variability of EASM, the role of natural external forcing including solar radiation and volcanic aerosols, the contribution of anthropogenic forcing (including emissions of greenhouse gases and aerosols). In addition, the thermodynamic and dynamic processes associated with climate sensitivity that are responsible for the uncertainties in climate change projections are also discussed. Both the strengths and weakness of the current state of the art climate models are documented. Instead of simply summarizing the models' performance, the review is done along with a discussion on our understanding of the strengths and weaknesses from the perspective of dynamical/physical processes. In the final part, we provide a list of potential ways to improve the models' performance, which includes the optimization of model parameters, improvement of model physics by coordinating model studies and field campaigns, and development of high-resolution and convection-permitting models.