In liquid crystal devices it is important to understand the physics underlying their switching between different states, which is usually achieved by applying or removing an electric field. Flow is known to be a key determinant of the timescales and pathways of the switching kinetics. Incorporating hydrodynamic effects into theories for liquid crystal devices is therefore important; however this is also highly non-trivial, and typically requires the use of accurate numerical methods. Here, we review some recent advances in our theoretical understanding of the dynamics of switching in liquid crystal devices, mainly gained through computer simulations. These results, as we shall show, uncover interesting new physics, and may be important for future applications.