We study the pricing of bank deposits in the Euro area during 2007--2024. We document that the pass-through of policy rates to sight deposit rates is low, asymmetric, varies across countries, and decreases over time. We estimate an equilibrium model of bank deposit markets, and find that depositors‘ price sensitivity exhibits large heterogeneity across EU markets and over time. Rate-sensitive depositors switched to higher-yielding savings products, decreasing the rate-sensitivity of the remaining pool of sight deposits and increasing banks‘ market power, accounting for the sluggish pass-through following the 2022 European Central Bank‘s rate hikes.