Erdos conjectured that a set of natural numbers of positive lower density contains the sum of two infinite sets. In this talk I will describe progress on the conjecture.  In particular, I will discuss the truth of the conjecture in the “high density” case and how this implies a “1-shift” version of the conjecture in general.  These aforementioned results use nonstandard analysis.  Time permitting,  I will also discuss the conjecture in model-theoretically tame contexts.