In many financial problems, small variations in some inputs may result in big changes in the outputs. In this talk, we consider the problem of portfolio selection as suggested by Markowitz. This model relies on a covariance matrix usually estimated using historical returns of the assets under consideration. Gross error in these returns or atypical events occurring in the past could lead to different portfolios with quite different expected returns. Defining methods that do not depend too much on these atypical data is the aim of robust statistics. We will show that some techniques developed in that field are worth applying in our context. More precisely, the covariance matrix of historical data will be estimated with the Minimum Covariance Determinant estimator, computed with a 'smooth' algorithm. This robust Markowitz methodology will be illustrated on real financial data.