The North American monsoon (NAM) is the principal driver of summer severe weather in the Southwest U.S. With sufficient atmospheric instability and moisture, monsoon convection initiates during daytime in the mountains and later may organize, principally into mesoscale convective systems (MCSs). Most monsoon-related severe weather occurs in association with organized convection, including microbursts, dust storms, flash flooding and lightning. The overarching theme of this dissertation research is to investigate simulation of monsoon severe weather due to organized convection within the use of regional atmospheric modeling. A commonly used cumulus parameterization scheme has been modified to better account for dynamic pressure effects, resulting in an improved representation of a simulated MCS during the North American monsoon experiment and the climatology of warm season precipitation in a long-term regional climate model simulation. The effect of urbanization on organized convection occurring in Phoenix is evaluated in model sensitivity experiments using an urban canopy model (UCM) and urban land cover compared to pre-settlement natural desert land cover. The presence of vegetation and irrigation makes Phoenix a "heat sink" in comparison to its surrounding desert, and as a result the modeled precipitation in response to urbanization decreases within the Phoenix urban area and increase on its periphery. Finally, analysis of how monsoon severe weather is changing in association with observed global climate change is considered within the context of a series of retrospectively simulated severe weather events during the period 1948-2010 in a numerical weather prediction paradigm. The individual severe weather events are identified by favorable thermodynamic conditions of instability and atmospheric moisture (precipitable water). Changes in precipitation extremes are evaluated with extreme value statistics. During the last several decades, there has been intensification of organized convective precipitation, but these events occur with less frequency. A more favorable thermodynamic environment for monsoon thunderstorms is the driver of these changes, which is consistent with the broader notion that anthropogenic climate change is presently intensifying weather extremes worldwide.