Results on extremal functions of some interpolation inequalities introduced by Caffarelli, Kohn and Nirenberg and of weighted logarithmic Hardy inequalities are briefly reviewed. Some results of radial symmetry or of symmetry breaking are sketched, which result in the statement of an open question. These notes are based on a collaboration with M. Esteban, M. Loss, G. Tarantello and A. Tertikas. oui