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The introduction of cloud-aerosol interactions in recently developed general circulation models (GCMs) has increased considerably the role played by specification of model parameters and emissions in the simulation of historical climate change, especially through their impact on radiative forcing. Concurrently, evidence that cumulus convection in GCMs is a key factor determining their climate sensitivities has mounted. This increased knowledge of how models control their historical climate change implies a reduction in the usefulness of simulations of historical climate change as independent tests of model realism. In this circumstance, it is essential that the model components dominating sensitivity and forcing have process-level credibility independent of the GCMs in which they are used. The importance of cumulus convection in determining climate sensitivity is particularly critical in this regard. Constraining basic aspects of convection such as entrainment with observations or robust process-level models is essential. New developments in cumulus parameterization offer the prospect of improving their physical robustness towards this end. This presentation will discuss several of these developments, including non-equilibrium and prognostic closures, increased emphasis on departures from the mean state in formulating cumulus dynamics and thermodynamics in parameterizations, scale-aware parameterizations, and new observations of cumulus dynamics as constraints on parameterizations.