There is a considerable literature in econometrics on varying coefficient regression models. Some of the proposed models are simple and parsimonious. However given that even the simplest varying coefficient model is more complex than the constant coefficient model, researchers need to be able to test the adequacy of the constant coefficient simplification. This paper surveys the literature on testing for the presence of varying regression coefficients. We outline the wide variety of tests that have been proposed and look in detail at comparisons of the properties of different tests. In general, the literature indicates that tests that take into account the one-sided nature of the testing problem do best. Therefore tests such as point optimal tests and locally most mean powerful tests typically have superior power properties relative to other available tests. The paper concludes with a review of the application of this methodology in two areas of empirical finance. These involve testing the time constancy of systematic risk in the market model and testing the unbiased prediction hypothesis in forward and futures markets.