This contribution is devoted to a review of some recent results on existence, symmetry and symmetry breaking of optimal functions for Caffarelli-Kohn-Nirenberg (CKN) and weighted logarithmic Hardy (WLH) inequalities. These results have been obtained in a series of papers of the authors in collaboration with M. del Pino et al. [in: Ann. Sc. Norm. Super. Pisa, Cl. Sci. (5) 7, No. 2, 313–341 (2008; Zbl 1179.26055); Adv. Nonlinear Stud. 9, No. 4, 713–726 (2009; Zbl 1182.26031); J. Funct. Anal. 259, No. 8, 2045–2072 (2010; Zbl 1209.26020); “Extremal functions for Caffarelli-Kohn-Nirenberg and logarithmic Hardy inequalities”, Proc. Edinburgh A (to appear), arXiv:1007.0309; Calc. Var. Partial Differ. Equ. 42, No. 3–4, 461–485 (2011; Zbl 1246.26014)] and are presented from a new viewpoint.