  In this survey paper we give an overview on some aspects of singularities of
algebraic varieties over an algebraically closed field of arbitrary
characteristic. We review in particular results on equisingularity of plane
curve singularities, classification of hypersurface singularities and
determinacy of arbitrary singularities. The section on equisingularity has its
roots in two important early papers by Antonio Campillo. One emphasis is on the
differences between positive and zero characteristic and on open problems.
