As information exists in various modalities in real world, effective interaction and fusion among multimodal information plays a key role for the creation and perception of multimodal data in computer vision and deep learning research. With superb power in modelling the interaction among multimodal information, multimodal image synthesis and editing have become a hot research topic in recent years. Different from traditional visual guidance which provides explicit clues, multimodal guidance offers intuitive and flexible means in image synthesis and editing. On the other hand, this field is also facing several challenges in alignment of features with inherent modality gaps, synthesis of high-resolution images, faithful evaluation metrics, etc. In this survey, we comprehensively contextualize the advance of the recent multimodal image synthesis & editing and formulate taxonomies according to data modality and model architectures. We start with an introduction to different types of guidance modalities in image synthesis and editing. We then describe multimodal image synthesis and editing approaches extensively with detailed frameworks including Generative Adversarial Networks (GANs), GAN Inversion, Transformers, and other methods such as NeRF and Diffusion models. This is followed by a comprehensive description of benchmark datasets and corresponding evaluation metrics as widely adopted in multimodal image synthesis and editing, as well as detailed comparisons of different synthesis methods with analysis of respective advantages and limitations. Finally, we provide insights into the current research challenges and possible future research directions. We hope this survey could lay a sound and valuable foundation for future development of multimodal image synthesis and editing. A project associated with this survey is available at https://github.com/fnzhan/MISE.