Dome C is likely to be the best site in the world for mm and sub-mm observations.In this paper we focus on what can be done from Dome C toinvestigate the detailed properties of the Cosmic MicrowaveBackground (CMB). Two experiment typologies are particularly promising:precision measurements of the polarization of the CMB, to confirmthe presence of an inflation phase in the very early universe, andhigh resolution measurements of the Sunyaev-Zeldovich effect (SZE) in clustersof galaxies, which can be used to investigate dark energy anddark matter in the Universe. Several important teams are currently carrying outexperiments of the first kind; Dome C is the location of the BRAIN experiment,which uses bolometric interferometry as the tool to producesensitive measurements with low systematic effects, and certainly orthogonalto the systematic effects of all other instruments currently developed to this purpose.Dome C will be an ideal location for a large dish telescope for mmand sub-mm measurements. In addition to cutting-edge sub-mm science,a telescope complementing SPT (in size and/or in frequency)will be ideal for special CMB observation, like the detection of non-Gaussian features,the measurement of relativistic effects in SZE, the measurement of the SZE resultingfrom the decay products of super-symmetric dark matter in selectedclusters.