Historically charge density waves have been associated with the notions of Fermi surface nesting and, at the transition temperature, a soft phonon mode. In this talk, I will present two cases that defy this common theme. First, I will show that TiSe2 undergoes a transition due to exciton condensation, which exhibits a soft mode of a different, electronic variety. Second, when driving the system away from equilibrium, the phase transition is mediated by topological defects. These defects allow for the formation of a charge density wave that does not occur in equilibrium. This light-induced charge density wave shows some unique properties that suggest that it is not just a trivial extension of an equilibrium one.