This special issue of the European Journal of Applied Mathematics is devoted to the ‘Liquid Crystal Theory and Modelling: Discussion Meeting’ that was held in Oxford on the 29th-30th October 2009. This international, interdisciplinary meeting was organised jointly by Dr Apala Majumdar (University of Oxford) and Prof. Nigel Mottram (University of Strathclyde) and was funded by OCCAM (Oxford Centre for Collaborative Applied Mathematics), the London Mathematical Society, Taylor and Francis and Cambridge University Press.