Cumulus convection parameterization (CCP) is a core component of numerical weather prediction (NWP) models, which includes triggering conditions, cloud models, closure schemes, and feedback mechanisms, along with their implicit assumptions. As NWP models increasingly operate at convection-permitting resolutions, improving the scale awareness of CCPs is essential for enhancing model performance across varying resolutions. This study aims to systematically review recent progress in scale-aware CCP and to clarify the underlying physical assumptions and methodological developments. Based on a comprehensive analysis of the iterative evolution of four commonly used convection parameterization schemes (i.e., Arakawa–Schubert, Kain–Fritsch, Grell, and Tiedtke) in operational models, three key advancements in scale-aware CCP are identified. First, the traditional assumption of a negligible convective area fraction has been relaxed, allowing a non-negligible convective area fraction. This is achieved by introducing an explicit updraft area fraction parameter linked to grid resolution, which establishes its quadratic relationship with vertical eddy transport and facilitates a unified parameterization framework. Second, the representation of multiscale atmospheric characteristics and interactions has been enhanced by developing resolution-dependent formulations for critical parameters. These parameters (e.g., convective adjustment timescales, entrainment and detrainment rates, convective available potential energy, convective inhibition, and grid-scale vertical velocity) are systematically integrated into triggering conditions, closure schemes, and cloud microphysical models. Third, the “no-net-mass transport” assumption is addressed to achieve improved physics–dynamics coupling. To compensate for convection-induced mass perturbations, convection parameterization schemes now directly incorporate convective mass sources/sinks into the continuity equation or spread subsidence to neighboring grid points. Finally, we reflect on fundamental challenges in understanding the multiscale interaction nature of scale-aware CCP and its associated requirements for refined cloud microphysical understanding, and outline future development directions.