In this talk we present a way of preserving the asymptotic error expansion of symmetric Runge-Kutta methods of arbitrary order and,at the same time,providing the necessary damping for stiff initial value problems.This process is called symmetrization and is achieved by a method called a symmetrizer.We begin with a brief account of the historical events leading to current work and present the underlying theory and construction of symmetrizers.We discuss implementing extrapolation with symmetrization and conclude with some recent numerical results.