Learning deep generative models for 3D shape synthesis is largely limited by the difficulty of generating plausible shapes with correct topology and reasonable geometry. Indeed, learning the distribution of plausible 3D shapes seems a daunting task for most existing holistic shape representation, given the significant topological variations of 3D objects even within the same shape category. Enlightened by the common view that 3D shape structure is characterized as part composition and placement, we propose to model 3D shape variations with a part-aware deep generative network which we call PAGENet. The network is composed of an array of per-part VAE-GANs, generating semantic parts composing a complete shape, followed by a part assembly module that estimates a transformation for each part to correlate and assemble them into a plausible structure. Through splitting the generation of part composition and part relations into separate networks, the difficulty of modeling structural variations of 3D shapes is greatly reduced. We demonstrate through extensive experiments that PAGENet generates 3D shapes with plausible, diverse and detailed structure, and show two prototype applications: semantic shape segmentation and shape set evolution.