Neural discrete representations are crucial components of modern neural networks. However, their main limitation is that the primary strategies such as VQ-VAE can only provide representations at the patch level. Therefore, one of the main goals of representation learning, acquiring conceptual, semantic, and compositional abstractions such as the color and shape of an object, remains elusive. In this paper, we present the first approach to semantic neural discrete representation learning. The proposed model, called Semantic Vector-Quantized Variational Autoencoder (SVQ), leverages recent advances in unsupervised object-centric learning to address this limitation. Specifically, we observe that a simple approach quantizing at the object level poses a significant challenge and propose constructing scene representations hierarchically, from low-level discrete concept schemas to object representations. Additionally, we suggest a novel method for training a prior over these semantic representations, enabling the ability to generate images following the underlying data distribution, which is lacking in most object-centric models. In experiments on various 2D and 3D object-centric datasets, we find that our model achieves superior generation performance compared to non-semantic vector quantization methods such as VQ-VAE and previous object-centric generative models. Furthermore, we find that the semantic discrete representations can solve downstream scene understanding tasks that require reasoning about the properties of different objects in the scene.