The paper is organized as follows. In the next section we describe in detail the version of Huber’s (1964) M-estimator that has been used in applied econometrics, and discuss its interpretation. Section 3 presents the results of simulation studies illustrating the pitfalls of using robust regression estimators when the errors are heteroskedastic and/or skewed. Section 4 revisits the study of Strömberg (2004) on the relation between mass media and public spending, and illustrates the importance of defining the location measure of interest and using a suitable estimator for it. Finally, Section 5 presents brief concluding remarks