Abstract: Uniformly finite homology is a coarse invariant for metric spaces; in particular, it is a quasi-isometry invariant for finitely generated groups. We give a general introduction to uniformly finite homology and discuss its relation to homology with l∞-coefficients. Then, we present an overview about known applications, in particular regarding questions about amenability and rigidity of groups. Finally, we present our calculation of uniformly finite homology of many amenable groups. http://wwwmath.uni-muenster.de/u/ag_kramer/index.php?name=TSWS13&menu=teesemi&lang=de