Recently, the text-to-image diffusion model has gained considerable attention from the community due to its exceptional image generation capability. A representative model, Stable Diffusion, amassed more than 10 million users within just two months of its release. This surge in popularity has facilitated studies on the robustness and safety of the model, leading to the proposal of various adversarial attack methods. Simultaneously, there has been a marked increase in research focused on defense methods to improve the robustness and safety of these models. In this survey, we provide a comprehensive review of the literature on adversarial attacks and defenses targeting text-to-image diffusion models. We begin with an overview of text-to-image diffusion models, followed by an introduction to a taxonomy of adversarial attacks and an in-depth review of existing attack methods. We then present a detailed analysis of current defense methods that improve model robustness and safety. Finally, we discuss ongoing challenges and explore promising future research directions. For a complete list of the adversarial attack and defense methods covered in this survey, please refer to our curated repository at https://github.com/datar001/Awesome-AD-on-T2IDM.