The talk starts with an overview of multivariate M-functionals of location and scatter, including symmetrized M-functionals of scatter. Then we discuss general properties of the underlying log-likelihood function. After that we review the currently known algorithms, fixed-point or iteratively reweighted moments. It is explained why these algorithms are intrinsically suboptimal: Then an alternative strategy, based on a "partial Newton" approach, is developed. Numerical examples and, if time permits, applications of M-estimators to Independent Component Analysis are presented.