Z' vector bosons with family dependent couplings may explain recent disagreements between Standard Model predictions and measurements involving certain B meson decays to muon pairs. We shall briefly summarise the relevant data and discuss the necessary properties of a simplified model involving the bosons. We then extend to a full U(1) model based on third family hypercharge, discussing the phenomenology. Z'->mu+ mu- collider searches are key, and we present bounds on the models presented by them.