  Let $K$ be a field equipped with a discrete valuation $v$. In a pioneering
work, S. MacLane determined all valuations on $K(x)$ extending $v$. His work
was recently reviewed and generalized by M. Vaqui\'e, by using the graded
algebra of a valuation. We extend Vaqui\'e's approach by studying residual
ideals of the graded algebra of a valuation as an abstract counterpart of
certain residual polynomials which play a key role in the computational
applications of the theory. As a consequence, we determine the structure of the
graded algebra of the discrete valuations on $K(x)$ and we show how these
valuations may be used to parameterize irreducible polynomials over local
fields up to Okutsu equivalence.
