The study of filamentous fungi can be difficult through experimental means alone due to the complexity of their natural growth habitat (e.g. soils) and the microscopic scale of growth (e.g. tip vesicle translocation and hyphal tip extension). Mathematical modelling provides a complimentary, powerful and efficient method of investigation. In this article, earlier mathematical models are briefly reviewed, before an overview of the construction and resultant predictions of a new model for fungal growth and function is given. Model predictions are compared to experimentally obtained data, giving new insight into the complex interaction between the developing mycelium and its environment.