Many aquatic environments have soft, muddy substrates, but this important property has largely been ignored in process-based models of turbidity currents. Previous turbidity current studies have focussed on flows over hard or non-cohesive, movable substrates. However, the flume experiments conducted in this study show that soft mud beds interact differently with a passing flow. Flow-bed interaction caused deformation and erosion of the beds and changed the flowstructure of the turbidity currents. Subsequently, these changes might impact the geometry of the resulting turbidite deposits. Five different interaction types between turbidity currents and soft substrates were defined: 1) no interaction, 2) interfacial waves, 3) mixing and erosion, 4) severe mixing and erosion, and 5) leading wave formation. The flow geometry and velocity, turbulence and concentration profiles of flows with no flow-bed interaction resembled those of flows over a hard substrate. But with increasing intensity of the flow-bed interaction, the friction at the flow-bed interface and erosion depth increased, the geometry of the front of the flow changed from blunt to pointed, and leading waves increased in size. This resulted in a decrease in the flow velocity, an increase in the height of the maximum velocity, an increase in near-bed turbulence, and an increase in flow concentration. These changes were strongest in the head of the flows, where the highest intensity of flow-bed interaction occurred. To study spatio-temporal changes in the flow structure of turbidity currents, a turbidity current model was created using image analysis on videos taken during the experiments. Results of the model indicated a trend in the head velocity of turbidity currents overriding a soft bed, with an initial decrease in flow velocity followed by an increase until a constant flow velocity was reached. The experimental results were summarised in flow-bed interaction phase diagrams which showed a decrease in flow-bed interaction with increasing yield strength of the bed and an increase in flow-bed interaction with an increase in bed shear stress. For the flow-bed concentration ratios used in this study, the bed shear stress had the largest influence on the flow-bed interaction. Fieldwork was conducted in the Grès de Peïra-Cava (France) which focussed on the lower bed boundary characteristics of turbidite deposits with an underlying mud bed. Flat, non-eroded bed boundaries were inferred to result from flows with no interaction with the bed, while wavy, non-eroded boundaries were believed to be an indication for interfacial wave interaction. Flame and loading structures were interpreted as products of mixing and erosion and sediment injections were related to leading waves, although no direct evidence for this was found in the field. Predictions of turbidite deposit geometry and composition based on the results of this study show a large variation in deposit thickness, run-out length and composition which is of great importance to the hydrocarbon industry.