Nematic liquid crystals are ubiquitous examples of partially ordered materials that combine the directionality of solids with fluidity. Nematics are anisotropic materials with distinguished material directions, referred to as "nematic directors". Nematics have long been the working material of choice for the flourishing liquid crystal display industry, because nematics have anisotropic optical and electromagnetic responses.
Nematics are now being used for innovative applications in sensors, actuators, diagnostic devices and nano-scale technologies. In this talk, we review the powerful continuum Landau-de Gennes theory for nematic liquid crystals. We present some case studies on the mathematical modelling of nematic-based multistable liquid crystal devices and compare theory with experimental results. We also discuss new directions in the mathematical modelling of confined nematic liquid crystalline systems, for interdisciplinary advances in the field.