It is well known that results in Ergodic Theory can be used to prove results in Additive Combinatorics.  An example is Szemeredi’s Theorem: A set of natural numbers of positive upper density contains arbitrarily long arithmetic progressions. In this survey talk I will explain how one can use limits along nilpotent ultrafilters to generalize such results.  This is a lecture I will be giving as part of a workshop on Ergodic Theory and Additive Combinatorics.  No knowledge of Ergodic Theory or Additive Combinatorics is required. I will present the necessary background.