Abstract: From my perspective these two topics became linked when Werner Mueller in 1998 observed that the Lifshitz-Krein spectral shift function from scattering theory calculated spectral flow in some problems involving Dirac type operators. Subsequently, using noncommutative analysis this link was strengthened in papers I wrote with Sukochev et al. Recently with the help of Jens Kaad's thesis I noticed a link betweenthe Witten index (a notion that was studied with the aid of the spectral shift function) and cyclic homology. This talk will aim for an overview of these developments.