  Let $(K,v)$ be a valued field. We review some results of MacLane and Vaqui\'e
on extensions of $v$ to valuations on the polynomial ring $K[x]$. We introduce
certain MacLane-Vaqui\'e chains of residually transcendental valuations, and we
prove that every valuation $\mu$ on $K[x]$ is a limit of a finite or countably
infinite MacLane-Vaqui\'e chain. This chain underlying $\mu$ is essentially
unique and contains arithmetic data yielding an explicit description of the
graded algebra of $\mu$ as an algebra over the graded algebra of $v$.
