The overarching goal of the train track theory for free group automorphisms is finding the "best" ways to represent an automorphism so as to read off its dynamical properties. In this talk I will describe the progress I made in developing the theory for injective endomorphisms. To some degree, it turns out nonsurjective endomorphisms have simpler dynamics -- a result that I found surprising. If time permits, I may mention how the result was used to characterize when ascending HNN extensions of free groups are word-hyperbolic.