Scientific experiments often generate a large number of measurements. Also in an industrial or business environment, the number of available variables for different products or customers may become huge, due to ever more powerful monitoring systems. Multivariate statistical modeling is typically used to understand better the relationships between different variables, but their use becomes cumbersome if a high number of variables is measured. In this case, the use dimension reduction techniques, becomes appropriate. Another issue is that a traditional multivariate approach is based on over-simplified models, like multivariate normality. The use of robust methods not depending on unrealistic model assumptions is indispensable, and allows extracting features and structures in the data in a reliable way. While robust methods are well established for dealing with simple models, as the regression and location-scale model, there is still work to do for more complicated, multivariate and non-linear models. Since atypical observations are frequently present when analyzing complex data sets, new robust methods need to be introduced. Practical implementation and computational feasibility are of major importance in robust data mining.