Mathematical studies of nematic liquid crystals address in general two rather different perspectives: that of fluid mechanics and that of calculus of variations. The former focuses on dynamical problems while the latter focuses on stationary ones. The two are usually studied with different mathematical tools and address different questions. The aim of this brief review is to give the practitioners in each area an introduction to some of the results and problems in the other area. Also, aiming

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... bridge the gap between the two communities, we will present a couple of research topics that generate natural connections between the two areas. This article is part of the theme issue 'Topics in mathematical design of complex materials'.