We develop a new framework for studying the implementation of monetary policy through the banking sector. Banks are subject to a maturity mismatch problem leading to precautionary holdings of reserves. Through various instruments, monetary policy alters tradeos banks face between lending, holding reserves, holding deposits and paying dividends. This translates into the real economy via eects on real interests and lending. We study how these instruments interact with shocks to the volatility in the payments system, bank losses, the demand for loans and with capital requirements. We use a calibrated version of the model to answer, quantitatively, why have banks held onto a substantial increase in reserves while not increasing lending since 2008.