Large Language Models (LLMs) have demonstrated remarkable capabilities across various fields, from natural language understanding to text generation. Compared to non-generative LLMs like BERT and DeBERTa, generative LLMs like GPT series and Llama series are currently the main focus due to their superior algorithmic performance. The advancements in generative LLMs are closely intertwined with the development of hardware capabilities. Various hardware platforms exhibit distinct hardware characteristics, which can help improve LLM inference performance. Therefore, this paper comprehensively surveys efficient generative LLM inference on different hardware platforms. First, we provide an overview of the algorithm architecture of mainstream generative LLMs and delve into the inference process. Then, we summarize different optimization methods for different platforms such as CPU, GPU, FPGA, ASIC, and PIM/NDP, and provide inference results for generative LLMs. Furthermore, we perform a qualitative and quantitative comparison of inference performance with batch sizes 1 and 8 on different hardware platforms by considering hardware power consumption, absolute inference speed (tokens/s), and energy efficiency (tokens/J). We compare the performance of the same optimization methods across different hardware platforms, the performance across different hardware platforms, and the performance of different methods on the same hardware platform. This provides a systematic and comprehensive summary of existing inference acceleration work by integrating software optimization methods and hardware platforms. We point out that three trends (multimodality, inference-time compute, and higher inference energy efficiency) are promising to redefine the capabilities of edge artificial intelligence systems. Our project is available at https://dai.sjtu.edu.cn/project.html.