An anisotropic (dichroic) optical cavity containing a self-focusing Kerr medium is shown to display a bifurcation between static--Ising--and moving--Bloch--domain walls, the so-called nonequilibrium Ising-Bloch transition (NIB). Bloch walls can show regular or irregular temporal behavior, in particular, bursting and spiking. These phenomena are interpreted in terms of the spatiotemporal dynamics of the extended patterns connected by the wall, which display complex dynamical behavior as well. Domain wall interaction, including the formation of bound states is also addressed.