The cyclic homology was invented 25 years ago. I will start with the definition and some motivations behind it. Then I will outline some recent developments, such as: Index theorems and higher Riemann-Roch theorems Characteristic classes, secondary classes of D-modules Algebraic structures on the cyclic complexes (the work of Tamarkin, Dolgushev and myself, as well as Kontsevich-Soibelman and Costello). I will try to make the talk as introductory as possible.