Deep generative modeling has emerged as a powerful tool for synthesizing realistic medical images, driving advances in medical image analysis, disease diagnosis, and treatment planning. This chapter explores various deep generative models for 3D medical image synthesis, with a focus on Variational Autoencoders (VAEs), Generative Adversarial Networks (GANs), and Denoising Diffusion Models (DDMs). We discuss the fundamental principles, recent advances, as well as strengths and weaknesses of these models and examine their applications in clinically relevant problems, including unconditional and conditional generation tasks like image-to-image translation and image reconstruction. We additionally review commonly used evaluation metrics for assessing image fidelity, diversity, utility, and privacy and provide an overview of current challenges in the field.