Much empirical research in economics and other fields is concerned with estimating the mean of a random variable conditional on one or more explanatory variables (conditional mean function). The most frequently used estimation methods assume that the conditional mean function is known up to a finite number of parameters, but the resulting estimates can be highly misleading if the assumed parametric model is incorrect. This paper reviews several semiparametric methods for estimating conditional mean functions. These methods are more flexible than parametric methods and offer greater estimation precision than do fully nonparametric methods. The various estimation methods are illustrated by applying them to data on the salaries of professional baseball players in the USA. We find that a parametric model and several simple semiparametric models fail to capture important features of the data. However, a sufficiently rich semiparametric model fits the data well. We conclude that semiparametric models can achieve their aim of providing flexible representations of conditional mean functions, but care is needed in choosing the semiparametric specification. Our analysis also provides some suggestions for further research on semiparametric estimation.