Statisticians have been trying to develop universal estimation techniques with good estimation properties. One of them is the Maximum Likelihood Estimation developed by Sir Ronald Fisher in the 1920’s. It has been very successful and is still widely used in practice nowadays. The MLE has excellent asymptotic properties on regular parametric models but it suffers from a certain lack of robustness. I will try to explain what “robustness” means with examples for which the MLE fails, and present what tools have been developed in order to achieve robust estimation.