In this work, we provide a systematic survey of Discrete Diffusion Language Models (dLLMs) and Discrete Diffusion Multimodal Language Models (dMLLMs). Unlike autoregressive (AR) models, dLLMs and dMLLMs adopt a multi-token, parallel decoding paradigm using full attention and a denoising-based generation strategy. This paradigm naturally enables parallel generation, fine-grained output control, and dynamic perception. These capabilities are previously difficult to achieve with AR models. A growing number of industrial-scale proprietary d(M)LLMs, as well as a large number of open-source academic d(M)LLMs, have demonstrated performance comparable to their autoregressive counterparts, while achieving up to 10$\times$ acceleration in inference speed. These developments position discrete diffusion models as a promising alternative to intelligence based on the traditional autoregressive approach. In this work, we present a comprehensive overview of the research in the dLLM and dMLLM domains. We trace the historical development of dLLMs and dMLLMs, formalize the underlying mathematical frameworks, list commonly-used modeling methods, and categorize representative models. We further analyze key techniques for training, inference, quantization. We also discuss the trustworthy issues and summarize emerging applications across language, vision-language, and biological domains and etc.. We conclude by discussing future directions for research and deployment. Relative papers are collected in https://github.com/LiQiiiii/Awesome-Discrete-Diffusion-LLM_MLLM