  Indices of vector fields on (complex analytic) singular varieties have been
considered by various authors from several different viewpoints. All these
indices coincide with the classical local index of Poincar\'e-Hopf when the
ambient variety is a smooth manifold. One has the Schwartz index, the local
Euler obstruction, the GSV-index, the virtual index and the homological index
(and probably other indices too). In this article we give a brief overview of
all these indices and the relations amongst them. We also indicate their
relations with the various generalisations to complex analytic singular
varieties of the Chern classes of complex manifolds.
