In the outer layers of the Sun (≈ 30% by radius), energy is transported by convection. The nature of the highly stratified and compressible convective flow is determined from the components of the energy flux (internal, kinetic, viscous, magnetic and radiative). Local suppressions or enhancements of any of these components may give rise to measurable changes in the emergent radiation.On the solar surface there is direct evidence for modulation of the emerging heat flux covering a large range in

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... spatial and temporal scales, particularly associated with concentrated magnetic fields (e.g. sunspots, plages). Associated with these surface features is the observation that the characteristics of convective motions are also modified. In the deeper layers, the interaction of convection and magnetic fields will play an important role in readjusting the local emerging heat flux and thus should contribute to the modulation of the total solar irradiance.The task of calculating the response of the convection zone structure to developing active regions, and the solar activity cycle in general is difficult and complex due to the highly non-linear nature of the interaction of convection and magnetic fields. Theoretical work has ranged from empirical and global structure models, all the way to fine scale compressible convection simulations. This paper will highlight some recent theoretical advances that may have a direct bearing on the understanding of solar luminosity and irradiance variations and outline the important problems that must be addressed and what observational constraints may be used.