Mathematical Modeling of Biofilms: Over 90% of bacterial biomass exists in the form of biofilms. The ability of bacteria to attach to surfaces and to form biofilms often is an important competitive advantage for them over bacteria growing in suspension. Some biofilms are "good" in natural and engineered systems; they are responsible for nutrient cycling in nature and are used to purify waters in engineering processes. Other biofilms are "bad" when they cause fouling and infections of humans and plants. Whether we want to promote good biofilms or eliminate bad biofilms, we need to understand how they work and what works to control them. Mathematical models help us understand the complex phenomena that occur in biofilms. In recent years, biofilm modelling has rapidly advanced, resulting in a diversity of modeling approaches and tools. On the one hand, complex three-dimensional biofilm models can describe many aspects of the formation of heterogeneous biofilms. On the other hand, it is not always necessary to use such complex models. Simple models - ones that can be solved easily with a spreadsheet sometimes provide the information we need. Mathematical Modeling of Biofilms provides guidelines for the selection and use of mathematical models of biofilms. The whole range of existing models -- from simple analytical expressions to complex numerical models -- is covered. The application of the models for the solution of typical problems is demonstrated, and the performance of the models is tested in comparative studies. With the dramatic evolution of the computational capacity still going on, modeling tools for research and practice will become more and more significant in the next few years. This report provides the foundation to understand the models and to select the most appropriate one for a given use. The different types of biofilm models are described and compared for specific applications. For example, mathematical models often are used to quantify substrate conversion in biofilm reactors used for water treatment. A different application is for describing how heterogeneous biofilms develop in time and space. Mathematical Modeling of Biofilms gives a state-of-the-art overview that is especially valuable for educating students, new biofilm researchers, and design engineers. Through a series of three benchmark problems, the report demonstrates how to use the different models and indicates when simple or highly complex models are most appropriate.