The concept of attractors, well-known in classical mechanics, proved very productive in the theory of black holes and inflationary cosmology. I will start with attractors in supersymmetric black holes and discuss how the discovery of Kaluza-Klein black hole attractors helped recently to explain the mysterious cancellation of ultraviolet divergences in 82 Feynman diagrams in 4-loop superamplitude in N=5 supergravity.
I will also describe inflationary alpha-attractors. This large class of inflationary models gives predictions that are stable with respect to even very significant modifications of inflationary potentials. These predictions match all presently available CMB-related cosmological data. Some of these models have a Kaluza-Klein origin and provide targets for the future satellite mission LiteBIRD, which will attempt to detect primordial gravitational waves. I will show that potentials in some of the recent advanced versions of cosmological attractors have a beautiful fractal landscape structure.