Solutions to many problems in number theory can be described using the theory of algebraic stacks. In this talk, I will describe a Diophantine equation, the so-called “generalized Fermat equation”, whose integer solutions correspond to points on an appropriate stacky curve: a curve with extra automorphisms at prescribed points. Using étale descent over such a curve, we characterize local and global solutions to a family of such equations and give asymptotics for the local-global principle in the corresponding family of stacky curves. This is joint work with Juanita Duque-Rosero, Chris Keyes, Manami Roy, Soumya Sankar and Yidi Wang.