Image synthesis has attracted emerging research interests in academic and industry communities. Deep learning technologies especially the generative models greatly inspired controllable image synthesis approaches and applications, which aim to generate particular visual contents with latent prompts. In order to further investigate low-level controllable image synthesis problem which is crucial for fine image rendering and editing tasks, we present a survey of some recent works on 3D controllable image synthesis using deep learning. We first introduce the datasets and evaluation indicators for 3D controllable image synthesis. Then, we review the state-of-the-art research for geometrically controllable image synthesis in two aspects: 1) Viewpoint/pose-controllable image synthesis; 2) Structure/shape-controllable image synthesis. Furthermore, the photometrically controllable image synthesis approaches are also reviewed for 3D re-lighting researches. While the emphasis is on 3D controllable image synthesis algorithms, the related applications, products and resources are also briefly summarized for practitioners.