We propose a neural reflectance model (NeuBRDF) that offers highly versatile material representation, yet with light memory and neural computation consumption towards achieving real-time rendering. The results depicted in Fig. 1, rendered at full HD resolution on a contemporary desktop machine, demonstrate that our system achieves real-time performance with a wide variety of appearances, which is approached by the following two designs. Firstly, recognizing that the bidirectional reflectance is distributed in a sparse high-dimensional space, we propose to project the BRDF into two low-dimensional components, i.e. two hemisphere feature-grids for incoming and outgoing directions, respectively. Secondly, we distribute learnable neural reflectance primitives on our highly-tailored spherical surface grid. These primitives offer informative features for each hemisphere component and reduce the complexity of the feature learning network, leading to fast evaluation. These primitives are centrally stored in a codebook and can be shared across multiple grids and even across materials, based on low-cost indices stored in material-specific spherical surface grids. Our NeuBRDF, agnostic to the material, provides a unified framework for representing a variety of materials consistently. Comprehensive experimental results on measured BRDF compression, Monte Carlo simulated BRDF acceleration, and extension to spatially varying effects demonstrate the superior quality and generalizability achieved by the proposed scheme.