Mortgage markets are central to monetary policy transmission. We show that this is because monetary policy impacts the supply of mortgage credit by the two largest mortgage holders: banks and the Federal Reserve. The Fed's supply of mortgage credit consists of buying or selling mortgage-backed securities (MBS) under its quantitative easing and tightening (QE and QT) programs. Banks' supply of mortgage credit is driven by the deposits channel of monetary policy. Under the deposits channel, when the Fed lowers rates, banks receive large inflows of deposits. They invest these deposits in long-term fixed-rate assets, in particular MBS, to match the interest-rate sensitivity of their income and expenses. The deposits channel reverses when the Fed raises rates: deposits flow out and banks sell MBS. Through the combined effect of QE/QT and the deposits channel, monetary policy drives mortgage rates, mortgage originations, and residential investment. We show that QE/QT and the deposits channel played a large role in the expansion and contraction of mortgage credit during the 2020--24 monetary policy cycle. Our results imply that monetary policy will continue to operate through these channels in future cycles.