Mixing and equilibration: Protagonists in the scene of nonextensive statistical mechanics

After a brief review of the present status of nonextensive statistical mechanics, we present a conjectural scenario where mixing (characterized by the entropic index $q_{mix} le 1$) and equilibration (characterized by the entropic index $q_{eq} ge 1$) play central and inter-related roles, and appear to determine {it a priori} the values of the relevant indices of the formalism. Boltzmann-Gibbs statistical mechanics is recovered as the $q_{mix}=q_{eq}=1$ particular case.