Jets at colliders like the LHC are incredibly complicated to understand, both theoretically and experimentally. In this talk, I describe a general class of jet shape observables, based on the Energy-Mover’s-Distance and its variants, that can be used to distill the information inside jets in experimentally, computationally, and theoretically tractable ways. These observables probe the geometric properties of jets in a human-interpretable way and are in-principle calculable using perturbative QCD. I also briefly discuss how theoretical guarantees and priors such as IRC-safety can be baked into machine learning models and loss functions, and how they can also be used to study the shape of jets