This paper develops and estimates a Quadratic-Gaussian model of the U.S. term structure that can accommodate the rich dynamics of inflation risk premia over the 1983-2013 period by allowing for time-varying market prices of inflation risk and incorporating survey information on inflation uncertainty in the estimation. The model captures changes in premia over very diverse periods, from the inflation scare episodes of the 1980s, when perceived inflation uncertainty was high, to the more recent episodes of negative premia, when perceived inflation uncertainty has been considerably smaller. A decomposition of the nominal ten-year yield suggests a decline in the estimated inflation risk premium of 1.7 percentage points from the early 1980s to mid 1990s. Subsequently, its predicted value has fluctuated around zero and turned negative at times, reaching its lowest values (about -0.6 percentage points) before the latest financial crisis, in 2005-2007, and during the subsequent weak recovery, in 2010-2012. The model's ability to generate sensible estimates of the inflation risk premium has important implications for the other components of the nominal yield: expected real rates, expected inflation, and real risk premia.