Cell dynamics simulations are a powerful tool to simulate kinetic processes
in phase separating systems. Here we review the technique and its applicat
ion to block copolymers. Its advantages and disadvantages compared to other
simulation methods for block copolymer structure and dynamics are reviewed
. Results on the dynamics of microphase separation and interface propagatio
n, and on the rate of order-order phase transitions are reviewed. The use o
f the method to model certain shear-induced structural and flow effects is
also summarised.