This paper surveys the growing literature on diagnostic testing of models based on unit record data. We argue that while many of these tests are produced in a Lagrange multiplier framework they are often more readily derived, and more easily applied, if approached from the conditional moment testing view of Newey (1985) and Tauchen (1985). In addition we propose some new tests based on comparisons of parametric estimators with nonparametric estimators which are consistent under certain forms of misspecification. To illustrate the utility of the tests we employ them in the examination of some existing published studies.