  In the nineties, several methods for dealing in a more efficient way with the
implicitization of rational parametrizations were explored in the Computer
Aided Geometric Design Community. The analysis of the validity of these
techniques has been a fruitful ground for Commutative Algebraists and Algebraic
Geometers, and several results have been obtained so far. Yet, a lot of
research is still being done currently around this topic. In this note we
present these methods, show their mathematical formulation, and survey current
results and open questions.
