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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, aimingdoi:10.1098/rsta.2020.0432 pmid:34024125 fatcat:g2twtrzrmjawjbxm7zjtgcvbaa