It is well known that the radiative heat flux exchanged between two hot bodies separated by a distance larger than their thermal wavelengths cannot be larger than the flux exchanged between two blackbodies at the same temperature. However at subwavelength distances, the heat flux can surpass the blackbody limit by several orders of magnitude due to the contribution of the evanescent electromagnetic field. In this case one can speak of super-Planckian thermal radiation. In this work we discuss in detail the origin of super-Planckian exchanges between multilayer materials and we propose different strategies to enhance them by tailoring the evanescent modes supported by these media.