The present state of understanding of the dynamics of magnetic domain walls and magnetic bubbles is reviewed. The theory of domain wall motion for the linear and non-linear regions is outlined. Experimental techniques for straight walls and magnetic bubbles are discussed. An extensive comparison between theory and experiment is made. Topics included are peak and saturation velocities, mobility, inertial effects and overshoot, hard bubbles, wall states and state transformations in magnetic bubbles. Origins of wall damping are also discussed.