Dynamics of the cellular pattern growth and rheology of foams are studied by means of computer simulations using simplified models, the so called vertex models which are constructed from a unified point of view. The vertex equations of motion for the pattern growth problem are derived from the curvature-driven interface model. Scaling behavior of the pattern growth is illustrated with the simulation results. For the rheology of foams a new vertex model is re-constructed considering the dissipation from the viscous fluid in the vicinity of Plateau borders. Two types of simulation are studied. One is performed under homogeneous shear. It is shown that the system possesses a finite yield stress and behaves like Bingham plastics. The role of topology change of the cellular structure is examined. Another is carried out for a fixed over all shear rate, where the velocity field is self-consistently determined. It is observed that for large strain regime stress releases occur intermittently and the power spectrum of the time series of stress shows a power law behavior.