Mapping tori of irreducible free group automorphisms are well-understood. In this talk, I will sketch the reason why the mapping torus of an irreducible nonsurjective free group endomorphism is word-hyperbolic. The proof uses various standard tools that are important in the study of low-dimensional dynamics and geometry: laminations on graphs, the Culler-Vogtmann outer space, and the Bestvina-Feighn combination theorem.