This paper is a critical survey of models designed for pricing xed income securities and their associated term structures of market yields. Our primary focus is on the interplay between the theoretical specication of dynamic term structure models and their empirical t to historical changes in the shapes of yield curves. We begin by overviewing the dynamic term structure models that have been t to treasury or swap yield curves and in which the risk factors follow diusions, jump-diusion, or have \switching regimes." Then the goodness-of-ts of these models are assessed relative to their abilities to: (i) match linear projections of changes in yields onto the slope of the yield curve; (ii) match the persistence of conditional volatilities, and the shapes of term structures of unconditional volatilities, of yields; and (iii) to reliably price caps, swaptions, and other xed-income derivatives. For the case of defaultable securities we explore the relative ts to historical yield spreads.