Bacterial biofilms are microbial depositions on immersed surfaces. They are ubiquitous in natural and engineered environments. For example, they play a significant role in medical applications where they can grow on artificial implants and cause infections; they form dental plaques and contribute to tooth decay; they can be utilized to assist in clean-up of contaminated soils or groundwater aquifers; they accelerate corrosion of metal surfaces; and they are a main culprit behind contamination of drinking water systems and food processing equipment. Two essential aspects in many of the application areas just indicated are the way in which a biofilm deforms in response to shearing forces, and whether it ultimately detaches in response to the applied shear. In food processing plants for example, detached patches of biofilm material enter the production stream and can cause severe (sometimes even fatal) health risks for consumers. We will combine techniques from mathematical modelling and analysis, experimentation and computation in order to study the growth, deformation and detachment of biofilms immersed in fluid. A biofilm is a complex viscoelastoplastic material that changes its mechanical behaviour in response to environmental conditions, and suitable rheological constitutive relations will have to be developed in order to capture realistic biofilm behaviours. We will not only validate our model results in laboratory experiments, but also develop efficient and accurate numerical algorithms that are capable of simulating realistic 3D scenarios representing the fluid-biofilm interaction. We expect that these computations will ultimately require the use of parallel computing resources and suitably parallelised versions of the underlying algorithms.