By a celebrated theorem of Faltings, a curve of genus 2 or more over the rationals has finitely many rational points. While Faltings’ proof does not construct the finite set of rational points, Kim’s nonabelian Chabauty program gives a finite superset of p-adic points, known as the Chabauty–Kim sets. We describe the computation of the Chabauty–Kim sets in various settings and examine the mock rational points (those finitely many points that are not rational) that may arise in these sets. Through- out, we present a number of examples. This is based on joint work with Alexander Betts.