The functor of p-typical Witt vectors is most well known for lifting perfect fields of characteristic p into complete discrete valuation rings. However, it is a well-defined functor on arbitrary rings; we will indicate how applying this functor to local rings of mixed characteristic gives some new perspectives on p-adic Hodge theory. We will also touch briefly upon some mysterious links to algebraic K-theory coming from the work of Hesselholt. Based on joint papers with Chris Davis (Copenhagen).