Abstract. As far as the representation of deep moist convection is concerned, only two kinds of model physics are used at present: highly parameterized as in the conventional general circulation models (GCMs) and explicitly simulated as in the cloud-resolving models (CRMs). Ideally, these two kinds of model physics should be unified so that a continuous transition of model physics from one kind to the other takes place as the resolution changes. With such unification, the GCM can converge to a global CRM (GCRM) as the grid size is refined. This paper suggests two possible routes to achieve the unification. ROUTE I continues to follow the parameterization approach, but uses a unified parameterization that is applicable to any horizontal resolutions between those typically used by GCMs and CRMs. It is shown that a key to construct such a unified parameterization is to eliminate the assumption of small fractional area covered by convective clouds, which is commonly used in the conventional cumulus parameterizations either explicitly or implicitly. A preliminary design of the unified parameterization is presented, which demonstrates that such an assumption can be eliminated through a relatively minor modification of the existing mass-flux based parameterizations. Partial evaluations of the unified parameterization are also presented. ROUTE II follows the "multi-scale modeling framework (MMF)" approach, which takes advantage of explicit representation of deep moist convection and associated cloud-scale processes by CRMs. The Quasi-3-D (Q3-D) MMF is an attempt to broaden the applicability of MMF without necessarily using a fully three-dimensional CRM. This is accomplished using a network of cloud-resolving grids with large gaps. An outline of the Q3-D algorithm and highlights of preliminary results are reviewed.