This document summarizes a presentation about the moduli space of BPS vortex-antivortex pairs. It discusses the O(3) sigma model on Euclidean space and compact domains. On Euclidean space, it derives Bogomol'nyi's equations and Taubes' equation to describe stationary solutions. It discusses the moduli space and derives a localization formula for the metric on moduli space. It also discusses vortex-antivortex collisions and the behavior of the conformal factor. On compact domains, it discusses an elliptic problem to describe solutions and derives a Bradlow bound on the number of vortices and antivortices.