The dynamics of thick domain walls are studied in the context of the classical field theory for a real scalar field. We treat, by numerically solving the equation of motion for the scalar field, the collision of two plane-symmetric walls as well as the collapse of walls that have spherical and cylindrical symmetry. Walls in both sine-Gordon and ${\ensuremath{\varphi}}^{4}$ theories are considered. We illustrate the striking and at times surprising differences between thin and thick walls. We also discuss the formation of black holes during spherical collapse.