The physics of soft matter - materials such as elastomers, gels, foams and liquid crystals - is an area of intense interest and contemporary study. Moreover, soft matter plays a role in a wide variety of important processes and application. For example, gel swelling and dynamics are an essential part of many biological and individual processes, such as motility mechanisms in bacteria and the transport and absorption of drugs. Ferroelectrics, liquid crystals, and elastomers are being used to design ever faster switching devices. Experimental studies, such as scattering, optical and electron microscopy, have provided a great deal of detailed information on structures. But the integration of mathematical modeling and analysis with experimental approaches promises to greatly increase our understanding of structure-property relationships and constitutive equations. The workshop on Modeling of Soft Matter has taken such an integrated approach. It brought together researchers in applied and computational mathematical fields such as differential equations, dynamical systems, analysis, and fluid and solid mechanics, and scientists and engineers from a variety of disciplines relevant to soft matter physics. An important outcome of the workshop has been to identify beautiful and novel scientific problems arising in soft matter that are in need of mathematical modeling and appear amenable to it and so to set the stage for further research. This volume presents a collection of papers representing the key aspects of the topics discussed at depth in the course of the workshop.