The sun is a magnetic star exhibiting both orderly and chaotic behavior in the magnetic fields that erupt into its atmosphere. These fields originate in the highly turbulent convection zone below the solar surface, with complex interactions between, rotation and magnetism contributing to dynamo action on multiple scales. New windows to study such intricate dynamics deep within the sun are provided by a combination of local-domain helioseismology carried out using Doppler imaging data from the SOHO spacecraft and of 3-D numerical simulations conducted on the latest breed of supercomputers. We discuss recent findings from helioseismology revealing large-scale subsurface flows that meander and evolve, and of their interaction with magnetic complexes. We contrast these with results from our team efforts in theoretical modelling of compressible convection within full spherical shells, showing the differential convection and propagating giant-cell convection that is realized, and of magnetic dynamo action that can be sustained. We comment on new initiatives with coupled computational domains that may permit greater fidelity in dealing with intense small-scale convection and dynamo processes close to the solar surface.
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