In the talk we describe two applications important for global climate and energy studies: methane hydrates and coalbed methane. Methane hydrates also known as "ice that burns" are present in large amounts along continental slopes and in permafrost regions and, therefore, are a possible source of energy and at the same time a potential environmental hazard. Their evolution critically depends on how the hydrate formation and dissociation affects the porescale properties. This so far has been only modeled with ad-hoc phenomenological approaches on top of the continuum models which account for multiple flowing phases, energy conservation, and phase change with or without latent heat. A similar situation arises in coalbed methane recovery where the traditional models of multicomponent adsorption appear inadequate to capture the dynamics of coupled porescale processes involving matrix swelling, competitive adsorption between carbon dioxide and methane, and adsorption hysteresis. Both applications have had comprehensive computational realizations based on coupled nonlinear PDE systems whose analysis has not yet been carried out. More importantly, both call for broadening the scope of modeling tools from traditional continuum PDE-based models to include a variety of discrete models which help to understand processes at porescale and to formulate constitutive relationships useful at continuum scale. In the talk we outline challenges of traditional continuum models, present some porescale results, and introduce some promising hybrid modeling approaches.