Fracton phases of matter are a class of three dimensional quantum phases characterised by excitations that exhibit restricted mobility. Although these phases share some features with conventional topological orders, such as locally indistinguishable ground states on non-trivial manifolds, they appear to lie outside existing paradigms for classifying or categorising quantum phases of matter. In this talk, I will introduce a new class of gapped three-dimensional models, dubbed “cage-net fracton models,” which host immobile fracton excitations in addition to non-Abelian particles with restricted mobility. These models are constructed from layers of 2D string-net models, whose spectrum includes non-Abelian anyons, by condensing “flux strings” built out of pointlike excitations. Through the example of the doubled-Ising cage-net model, I will demonstrate the existence of strictly immobile Abelian fractons and of non-Abelian particles restricted to move only along one dimension. In this model, the restricted-mobility non-Abelian excitations can be shown to be a fundamentally three-dimensional phenomenon, as they cannot be understood as bound states among two-dimensional non-Abelian anyons and Abelian particles. Finally, I will discuss generalisations and other non-Abelian fracton models, as well some open questions.