  The Minimum Covariance Determinant (MCD) method is a highly robust estimator
of multivariate location and scatter, for which a fast algorithm is available.
Since estimating the covariance matrix is the cornerstone of many multivariate
statistical methods, the MCD is an important building block when developing
robust multivariate techniques. It also serves as a convenient and efficient
tool for outlier detection. The MCD estimator is reviewed, along with its main
properties such as affine equivariance, breakdown value, and influence
function. We discuss its computation, and list applications and extensions of
the MCD in applied and methodological multivariate statistics. Two recent
extensions of the MCD are described. The first one is a fast deterministic
algorithm which inherits the robustness of the MCD while being almost affine
equivariant. The second is tailored to high-dimensional data, possibly with
more dimensions than cases, and incorporates regularization to prevent singular
matrices.
