We introduce the class of linear‐rational term structure models in which the state price density is modeled such that bond prices become linear‐rational functions of the factors. This class is highly tractable with several distinct advantages: (i) ensures nonnegative interest rates, (ii) easily accommodates unspanned factors affecting volatility and risk premiums, and (iii) admits semi‐analytical solutions to swaptions. A parsimonious model specification within the linear‐rational class has a very good fit to both interest rate swaps and swaptions since 1997 and captures many features of term structure, volatility, and risk premium dynamics—including when interest rates are close to the zero lower bound.