  We investigate the planarity of the boundaries of right-angled Coxeter
groups. We show that non-planarity of the defining graph does not necessarily
imply non-planarity of every boundary of the associated right-angled Coxeter
group, although it does in many cases. Our techniques yield a characterization
of the triangle-free defining graphs such that the associated right-angled
Coxeter group has boundary a Menger curve.
