In many situations bacteria aggregate to form biofilms: dense, surface-associated, three-dimensional structures populated by cells embedded in matrix. Biofilm architectures are sculpted by mechanical processes including cell growth, cell-cell interactions and external forces. Using single-cell live imaging in combination with simulations we characterize the cell-cell interactions that generate Vibrio cholerae biofilm morphologies. Furthermore, we show how external fluid flow changes the intrinsic local order and the global morphology of growing biofilms. Our results demonstrate the importance of cell dynamics mediated by adhesion proteins and matrix generation in determining the global architecture of biofilm structures.