Given a complex vector space V, consider the ring of polynomial 
functions on the space of configurations of a vectors and b 
covectors which are invariant under the natural action of SL(V). 
Rings of this type play a central role in representation theory, 
and their study dates back to Hilbert. Over the last three 
decades, different bases of these spaces were found. To explicitly 
construct, as well as to compare, some of these remarkable bases 
remains a challenging problem, already open when V is 3-dimensional.

In this talk, I report on recent developments in this theory in 
the 3-dimensional setting.