Despite decades of research and advancements in theoretical understanding, the capability of many Earth system models (ESMs) in simulating the Madden-Julian oscillation (MJO) and other tropical convectively coupled disturbances remains unsatisfactory.  Though emergent in the deep tropics, these disturbances strongly modulate global precipitation and temperature extremes, tropical cyclone activity, and monsoon systems, resulting in profound socio-economic impacts.  Given these hazards and the inadequate model predictive skill, improving the representation of organized tropical convection in ESMs is essential.  Here, we examine tropical subseasonal convective variability in E3SM versions 2 (E3SMv2) and 3 (E3SMv3) using process-oriented diagnostics designed to highlight key feedbacks among convection, moisture, and radiation.  Compared to its predecessor E3SM version (E3SMv1), E3SMv2 exhibits improvement in MJO amplitude, the coupling between moist convection and circulation (a fundamental feature of tropical atmospheric waves), the tropical precipitation diurnal cycle phase, and convection-radiation feedbacks.  Several model biases remain apparent in E3SMv2, however, including an overestimated MJO propagation speed, tropical precipitation diurnal cycle amplitude, and atmospheric Kelvin wave amplitude.  Preliminary analyses of E3SMv3 shows considerably more realistic mixed Rossby-gravity waves and atmospheric Kelvin waves, key drivers of the quasi-biennial oscillation (QBO).  Phenomenological changes are examined in the context of model configuration updates related to treatments of atmospheric instability, deep convective triggering, and convective organization.  These detailed diagnostics serve as an additional data point for the modeling community, providing insight on both E3SM model biases and driving mechanisms of tropical subseasonal convective variability.