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Generative models aim to learn the distribution of observed data by generating new instances. With the advent of neural networks, deep generative models, including variational autoencoders (VAEs), generative adversarial networks (GANs), and diffusion models (DMs), have progressed remarkably in synthesizing 2D images. Recently, researchers started to shift focus from 2D to 3D space, considering that 3D data is more closely aligned with our physical world and holds immense practical potential. However, unlike 2D images, which possess an inherent and efficient representation (\textit{i.e.}, a pixel grid), representing 3D data poses significantly greater challenges. Ideally, a robust 3D representation should be capable of accurately modeling complex shapes and appearances while being highly efficient in handling high-resolution data with high processing speeds and low memory requirements. Regrettably, existing 3D representations, such as point clouds, meshes, and neural fields, often fail to satisfy all of these requirements simultaneously. In this survey, we thoroughly review the ongoing developments of 3D generative models, including methods that employ 2D and 3D supervision. Our analysis centers on generative models, with a particular focus on the representations utilized in this context. We believe our survey will help the community to track the field's evolution and to spark innovative ideas to propel progress towards solving this challenging task.