  Smectic liquid crystals are materials formed by stacking deformable, fluid
layers. Though smectics prefer to have flat, uniformly-spaced layers, boundary
conditions can impose curvature on the layers. Since the layer spacing and
curvature are intertwined, the problem of finding minimal configurations for
the layers becomes highly nontrivial. We discuss various topological and
geometrical aspects of these materials and present recent progress on finding
some exact layer configurations. We also exhibit connections to the study of
certain embedded minimal surfaces and briefly summarize some important open
problems.
