  We review strategies to unveil the primordial large-$x$ structure of the
nucleons as well as the pion from hard-scattering experiments. Ideas are
presented for learning about the $x\to 1$ limit of nonperturbative QCD dynamics
at energy scales of order 1 GeV from collider experiments at much higher
scales. The behavior of parton distributions at $x\to 1$ predicted by the quark
counting rules and other low-energy theoretical approaches is contrasted with
phenomenological PDFs. Polynomial mimicry of PDF parametrizations is one of
many factors that influence the apparent power of the $(1-x)$ falloff. We
discuss implications of the mimicry for the large-$x$ falloff of the pion PDFs.
