As early as 1979 Apostol did pioneering work in applying Dual algebra theory to algebras generated by N-tuples of commuting contractions. Nevertheless progress has been considerably slower than in the case of single contractions. For instance, the initial 1979 Brown-Chevreau-Pearcy result (every contraction with spectrum dominating in the open unit disk has invariant subspaces) is still waiting for its "optimal" generalization (even for pairs of commuting contractions). This last talk will outline some of the progress made in the past 20 years including the breakthrough made in 1997 by Eschmeier (every commuting N-tuple of contractions having Harte spectrum dominating in the polydisk and admitting a unitary dilation has invariant subspaces) and illustrating the difficulties in the path to further progress. Indeed obstacles are met in each of the main fields which generally interplay when applying Dual algebra theory , in particular standard "geometrical" spectral theory, dilation theory, complex function theory. Corresponding open questions will be presented along the way.