  This paper is an extended version of the talk given by Miguel Olalla at the
International Conference on Valuation Theory in El Escorial in July 2011. Its
purpose is to provide an introduction to our joint paper "Extending a valuation
centered in a local domain to the formal completion" (Proc. London Math. Soc.
(2012) 105 (3), 571-621) without grinding through all of its technical details.
