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The Banff International Research Station will host the "Modelling of Thin Liquid Films - Asymptotic Approach vs. Gradient Dynamics" workshop in Banff from April 28, 2019 to May 3, 2019. Thin films and shallow droplets of liquids on (soft) solid or liquid substrates are ubiquitous in nature and technology. We find them on window panes and plant leaves when it rains. Thin liquid films line our lungs and form the tear film that protects our eyes, as well as being essential for various coating and printing techniques. Mathematicians, physicists and engineers have been studying the dynamics of drops and liquid films for a long time and have developed approximate models, the so called thin-film equations, that are easier to solve than more exact models. Thin-film equations can be derived and motivated in two different ways - one based on an exact mathematical (asymptotic) analysis of the basic transport equations of physico-chemical hydrodynamics and the other based on arguments from nonequilibrium thermodynamics and statistical physics. The results obtained with the two methods often agree but not always; and disagreement is common when the methods are applied to complex liquids relevant in modern applications. The workshop will bring together experts from Applied Mathematics, Theoretical and Experimental Physics and Engineering disciplines to discuss the fundamental issues underlying these discrepancies and will instigate the development of techniques to combine the approaches in a consistent way. Specifically, the scientists will consider two related questions that must be resolved when establishing new thin-film models: Which modelling strategy should be followed, i.e., is it more important that a model is mathematically rigorous or that it is consistent with nonequilibrium thermodynamics? The Banff International Research Station for Mathematical Innovation and Discovery (BIRS) is a collaborative Canada-US-Mexico venture that provides an environment for creative interaction as well as the exchange of ideas, knowledge, and methods within the Mathematical Sciences, with related disciplines and with industry. The research station is located at The Banff Centre in Alberta and is supported by Canada-s Natural Science and Engineering Research Council (NSERC), the U.S. National Science Foundation (NSF), Alberta-s Advanced Education and Technology, and Mexico-s Consejo Nacional de Ciencia y Tecnología (CONACYT).