Streptomyces are filamentous bacteria that are commonly found in soil ecosystems. During their complex life cycle Streptomyces produce many useful bioactive secondary metabolites. During growth in liquid cultures, filamentous, multicellular growth of Streptomyces can result in inefficient industrial antibiotic fermentations. Streptomyces form large heterogeneous aggregates in liquid culture where the morphology and metabolism of hyphae are influenced by external oxygen and nutrient profiles within a pellet. Understanding the features and emergent properties of these could significantly aid improvement of industrial-scale processes. This thesis studies the heterogeneous nature of hyphal growth by constructing a discrete-continuum hybrid stochastic differential equation model of filamentous growth and pellet formation. The model requires relatively few values for parameterisation of which many can be derived from experiments. The model is experimentally validated and tested, through analysis of growth curve data, coupled with manual and automated image analysis. Using enhanced green fluorescent protein fusions it was possible to study the spatio-temporal localization of proteins in key cellular processes inside pellets and relate these to pellet behaviour. The model delivers realistic simulations of Streptomyces pellet formation and is able to predict features, such as the density of hyphae, the number of tips and the location of metabolic switch within a pellet in response to external nutrient supply, which are almost impossible to do in all but the smallest aggregates. Using the antibiotic-producing soil bacterium Streptomyces as a model we have developed a flexible mathematical model platform. The model is scalable and will find utility and application in a range of branched biological networks such as fungal hyphal networks, plant root growth and angiogenesis.