  The ``Seifert Conjecture'' stated, ``Every non-singular vector field on the
3-sphere ${\mathbb S}^3$ has a periodic orbit''. In a celebrated work, Krystyna
Kuperberg gave a construction of a smooth aperiodic vector field on a plug,
which is then used to construct counter-examples to the Seifert Conjecture for
smooth flows on the 3-sphere, and on compact 3-manifolds in general. The
dynamics of the flows in these plugs have been extensively studied, with more
precise results known in special ``generic'' cases of the construction.
Moreover, the dynamical properties of smooth perturbations of Kuperberg's
construction have been considered. In this work, we discuss the genesi of
Kuperberg's construction as an evolution from the Schweitzer construction of an
aperiodic plug. We discuss some of the known results for Kuperberg flows, and
discuss some of the many interesting questions and problems that remain open
about their dynamical and ergodic properties.
