Flocks of birds, schools of fish, mixtures of motors and cytoskeletal filaments, swimming bacteria and driven granular media are systems of interacting motile units that exhibit collective behaviour. These can all be described as active matter systems, since each individual unit takes energy from an internal energy depot and transduces it into work performed on the environment. We review a model for cyanobacterial phototaxis, emphasising the differences from other models for collective behaviour in active matter systems. The interactions between individual cells during phototaxis are dominated by mechanical forces mediated by their physical attachments through type IV pili (T4P) and through the production of “slime”, a complex mixture of non-diffusible polysaccharides deposited by cells that acts to decrease friction locally. The slime, in particular, adds a component to the interaction that is local in space but non-local in time, perhaps most comparable to the pheromones laid down in ant trails. Our results suggest that the time-delayed component of the interactions between bacteria qualify their description as a novel active system, which we refer to as “damp” active matter.