Volumetric additive manufacturing is a novel fabrication method allowing rapid, freeform, layer-less 3D printing. Analogous to computer tomography (CT), the method projects dynamic light patterns into a rotating vat of photosensitive resin. These light patterns build up a three-dimensional energy dose within the photosensitive resin, solidifying the volume of the desired object within seconds. Departing from established sequential fabrication methods like stereolithography or digital light printing, volumetric additive manufacturing offers new opportunities for the materials that can be used for printing. These include viscous acrylates and elastomers, epoxies (and orthogonal epoxy-acrylate formulations with spatially controlled stiffness) formulations, tunable stiffness thiol-enes and shape memory foams, polymer derived ceramics, silica-nanocomposite based glass, and gelatin-based hydrogels for cell-laden biofabrication. Here we review these materials, highlight the challenges to adapt them to volumetric additive manufacturing, and discuss the perspectives they present.