In this chapter we consider the subject of robust statistics and, in particular, robust parameter estimation. Robust statistics is defined as statistical methods which are relatively insensitive to the presence of outliers. We start by discussing robust techniques which reduce the influence of outliers without actually identifying the outliers. We show how we may robustify the Bayesian paradigm by using likelihood functions with enhanced tails.Robust statisticsdefinition As an example we consider the Student-t mixture model which is a robust Gaussian mixture model. Finally we consider robust statistics in computer vision including robust subspace methods.