Experimental observations and some theoretical models for the propagation of ferroelastic domain boundaries and phase fronts are reviewed. While the static configurations of domains and domain walls are reasonably well understood in ferroelastics (and specifically in shape memory alloys), one finds that the dynamic features have been less thoroughly investigated. In most cases, a smooth movement of domain walls in the ballistic limit is observed, accelerated propagation seems not to exist in the time and space limits of most experiments. Pattern formation occurs when the local order parameter is conserved over a length scale which is different from the ferroelastic correlation length. Currently, only few spiky elastic measurements and domain wall jamming in ferroelastics have been reported. Emphasis is given to disordered systems in which the occurrence of 'jerky elasticity' can be expected.