Ultrafilters show up in many places, including logic, topology, and analysis. Despite this, the concept does not seem to be well-known among mathematicians (indeed, the speaker completed several years of graduate school without learning about them). The goal of this talk is to present a friendly introduction to ultrafilters and to highlight a few of their various manifestations. If all goes well, the talk will include a topological proof of Arrow’s Impossibility Theorem, a classic result from political science.