  We consider few-body bound state systems and provide precise definitions of
Borromean and Brunnian systems. The initial concepts are more than a hundred
years old and originated in mathematical knot-theory as purely geometric
considerations. About thirty years ago they were generalized and applied to the
binding of systems in nature. It now appears that recent generalization to
higher order Brunnian structures may potentially be realized as laboratory made
or naturally occurring systems. With the binding energy as measure, we discuss
possibilities of physical realization in nuclei, cold atoms, and condensed
matter systems. Appearance is not excluded. However, both the form and the
strengths of the interactions must be rather special. The most promising
subfields for present searches would be in cold atoms because of external
control of effective interactions, or perhaps in condensed-matter systems with
non-local interactions. In nuclei, it would only be by sheer luck due to a lack
of tunability.
