  Dual presentations of Coxeter groups have recently led to breakthroughs in
our understanding of affine Artin groups. In particular, they led to the proof
of the $K(\pi, 1)$ conjecture and to the solution of the word problem. Will the
"dual approach" extend to more general classes of Coxeter and Artin groups? In
this paper, we describe the techniques used to prove the $K(\pi, 1)$ conjecture
for affine Artin groups and we ask a series of questions that are mostly open
beyond the spherical and affine cases.
