The goal of p-adic non-abelian Hodge theory is to study p-adic representations of fundamental groups of varieties with methods from p-adic Hodge theory. In this talk, I will first explain how v-vector bundles arise naturally in this context. I will then explain how we can relate v-vector bundles to Higgs bundles via the p-adic Simpson correspondence. I will then sketch how in joint work with Daxin Xu, we interpret this correspondence more geometrically as a twisted isomorphism between the moduli spaces of either side.