Diffusion models, which leverage stochastic processes to capture complex data distributions effectively, have shown their performance as generative models, achieving notable success in image-related tasks through iterative denoising processes. Recently, diffusion models have been further applied and show their strong abilities in planning tasks, leading to a significant growth in related publications since 2023. To help researchers better understand the field and promote the development of the field, we conduct a systematic literature review of recent advancements in the application of diffusion models for planning. Specifically, this paper categorizes and discusses the current literature from the following perspectives: (i) relevant datasets and benchmarks used for evaluating diffusion modelbased planning; (ii) fundamental studies that address aspects such as sampling efficiency; (iii) skill-centric and condition-guided planning for enhancing adaptability; (iv) safety and uncertainty managing mechanism for enhancing safety and robustness; and (v) domain-specific application such as autonomous driving. Finally, given the above literature review, we further discuss the challenges and future directions in this field.