We investigate the use of neural fields for modelling diverse mesoscale structures, such as fur, fabric and grass. Instead of using classical graphics primitives to model the structure, we propose to employ a versatile volumetric primitive represented by a neural reflectance field (NeRF-Tex), which jointly models the geometry of the material and its response to lighting. The NeRF-Tex primitive can be instantiated over a base mesh to 'texture' it with the desired meso and microscale appearance. We condition the reflectance field on user-defined parameters that control the appearance. A single NeRF texture thus captures an entire space of reflectance fields rather than one specific structure. This increases the gamut of appearances that can be modelled and provides a solution for combating repetitive texturing artifacts. We also demonstrate that NeRF textures naturally facilitate continuous level-of-detail rendering. Our approach unites the versatility and modelling power of neural networks with the artistic control needed for precise modelling of virtual scenes. While all our training data are currently synthetic, our work provides a recipe that can be further extended to extract complex, hard-to-model appearances from real images.