Much recent work in ergodic theory has been motivated by interactions with other fields, including additive combinatorics, number theory, and harmonic analysis. A highlight of this interaction has been the study of patterns in certain subsets of the integers, starting with Szemeredi's Theorem on arithmetic progressions in sets of positive upper density and Furstenberg's subsequent proof of this using ergodic theory. This opened new questions in ergodic theory, and remarkably, it turns out that algebraic constraints (nilsystems) play a key role in governing these phenomena. In turn, these developments have led to breakthroughs in additive combinatorics and once again, nilsystems play a prominent role. I will give an overview of recent developments in these interrelated areas.