In lyotropic systems, four different isotropic phases may coexist with several cubic phases having different topologies and/or symmetries. We review here faceting phenomena, rising new conceptual issues, that have been recently found to occur at different cubic/isotropic interfaces: 1 degrees- depending on their tension, these interfaces can be either rich or poor in facets or even completely rough, 2 degrees- when facets coexist with rough surfaces, facets can grow due to the redistribution of the surfactant in the crystal, 3 degrees- upon a temperature cycling, ratchet-like growth of facets, until an elimination of rough surfaces takes place, 4 degrees- asymmetric crystal shapes are induced by temperature gradients, 5 degrees-rough surfaces "melt" prior to facets that stay "dry".