  Summation methods play a very important role in quantum field theory because
all perturbation series are divergent and the expansion parameter is not always
small. A number of methods have been tried in this context, most notably Pade
approximants, Borel--Pade summation, Borel transformation with mapping, which
we briefly describe and one on which we concentrate here, Order-Dependent
Mapping (ODM). We recall the basis of the method, for a class of series we give
intuitive arguments to explain its convergence and illustrate its properties by
several simple examples. Since the method was proposed, some rigorous
convergence proofs were given. The method has also found a number of
applications and we shall list a few.
