Bacterial biofilms pose a large threat to health. To understand this resilient and coordinated form of bacterial growth in more detail the bacterial cells' membrane potentials were studied. In circular Bacillus subtilis biofilms, in addition to previously described electrophysiological waves, which travelled from the centre of the biofilm out to the edge (centrifugal), waves which travelled from the edge of the biofilms towards the centre (centripetal) were also observed. New data analysis techniques and an agent-based fire-diffuse-fire model were used to show that the spatial heterogeneity in bacterial cell placements and curvature affected the propagation of wavefronts through the biofilm. The membrane potentials and physical responses of Pseudomonas aeruginosa and B. subtilis biofilms to 405 nm light were also investigated. It was found that all cells exhibited membrane potential hyperpolarisations in response to 405 nm light. The dynamics of these membrane potential changes depended on the stage of biofilm growth. At the early stages of biofilm growth, cells also dispersed in response to 405 nm light. A Hodgkin-Huxley style model was used to demonstrate that changes observed during biofilm growth could explain the observed differences in membrane potential dynamics. The secondary messenger cyclic di-guanosine monophosphate (c-di-GMP) is a crucial regulator in biofilm growth in P. aeruginosa. Its role in regulating the oxidative stress response of P. aeruginosa and the connection between c-di-GMP levels and membrane potential were investigated using a fluorescence-based GFP reporter strain. Oxidative stress induced changes in GFP and therefore the GFP-based reporter could not be reliably used to measure the c-di-GMP levels at high levels of oxidative stress. At low levels of oxidative stress, the reporter strain was used to show that oxidative stress induced an increase in the levels of c-di-GMP. This indicates that P. aeruginosa does regulate oxidative stress via this intracellular messenger and provides a mechanism that drives the dispersal response of P. aeruginosa to 405 nm light. Overall, it was shown that bacteria regulate their membrane potentials in response to a range of different stresses. The data analysis and modelling techniques developed in this thesis can be used to further study this emerging field of bacterial electrophysiology.