  The classical knot groups are the fundamental groups of the complements of
smooth or piecewise-linear (PL) locally-flat knots. For PL knots that are not
locally-flat, there is a pair of interesting groups to study: the fundamental
group of the knot complement and that of the complement of the ``boundary
knot'' that occurs around the singular set, the set of points at which the
embedding is not locally-flat. If a knot has only point singularities, this is
equivalent to studying the groups of a PL locally-flat disk knot and its
boundary sphere knot; in this case, we obtain a complete classification of all
such group pairs in dimension $\geq 6$. For more general knots, we also obtain
complete classifications of these group pairs under certain restrictions on the
singularities. Finally, we use spinning constructions to realize further
examples of boundary knot groups.
