With increasing use of high resolution (convection-permitting) models for numerical weather prediction and climate simulation, microphysics has moved to the forefront in terms of physical parameterizations. This is because without the use oftraditional convection parameterizations in these models, microphysicsis directly coupled to the convective dynamics. An overview of current approaches for representing microphysics will be given, as well asrecent efforts to improve parameterizations and some of the key remaining challenges. Impacts of microphysics on convection-permitting model simulations of deep convection will be presented, including impacts on cold pool evolution and storm structure. Particular attention will be paid to uncertainties arising from poorly-constrained process rates and parameters in the context of complex interactions between the microphysics and dynamics. Sensitivity to microphysics will also be compared to sensitivity from other aspects such as model grid resolution. Finally, new "outside-the-box" ideas and approaches for representing microphysics, representing a significant shift fromtraditional approaches, will be discussed.