In many applications of computer graphics, art, and design, it is desirable for a user to provide intuitive non-image input, such as text, sketch, stroke, graph, or layout, and have a computer system automatically generate photo-realistic images according to that input. While classically, works that allow such automatic image content generation have followed a framework of image retrieval and composition, recent advances in deep generative models such as generative adversarial networks (GANs), variational autoencoders (VAEs), and flow-based methods have enabled more powerful and versatile image generation approaches. This paper reviews recent works for image synthesis given intuitive user input, covering advances in input versatility, image generation methodology, benchmark datasets, and evaluation metrics. This motivates new perspectives on input representation and interactivity, cross fertilization between major image generation paradigms, and evaluation and comparison of generation methods.