The fed funds rate is basically banks borrowing from each other to meet nightly reserve requirements. The fed open market iterations steps in and buys/sells that overnight debt creating/destroying money in the process. After QE it now does a lot more of this on the long end too. The fed only really influences that rate, and it does go off script.

The link between the overnight rate and longer maturities has always been tenuous. Banks borrow I the short end, consumers on the longer end. Before QE, the Fed often had a difficult time pushing the long end around, but with QE it just did it direct.