This paper reviews recent advancements and research directions aimed at addressing the challenges of training and deploying Large Language Models (LLMs). It begins by discussing algorithm-level acceleration techniques to optimize LLM inference speed and resource utilization. The paper then explores LLM-hardware co-design strategies to improve system efficiency by tailoring hardware architectures to LLM requirements. Additionally, it delves into LLM-to-accelerator compilation approaches, involving customizing hardware accelerators for efficient LLM deployment. Finally, the paper examines LLM-aided design methodologies, focusing on High-Level Synthesis (HLS) functional verification, by creating a new dataset that contains a large number of buggy and bug-free codes. The authors propose novel solutions such as Medusa, a parallel decoding framework, and SnapKV, a method for reducing KV cache size, to enhance LLM efficiency and performance. They also discuss future research directions, including enhanced versatility in parallel decoding, combining KV compression with parallel decoding, and reconfigurable and heterogeneous hardware for LLMs. The paper concludes with a comprehensive overview of these advancements and future directions, aiming to pave the way for more efficient and scalable deployment of LLMs across diverse applications.This paper reviews recent advancements and research directions aimed at addressing the challenges of training and deploying Large Language Models (LLMs). It begins by discussing algorithm-level acceleration techniques to optimize LLM inference speed and resource utilization. The paper then explores LLM-hardware co-design strategies to improve system efficiency by tailoring hardware architectures to LLM requirements. Additionally, it delves into LLM-to-accelerator compilation approaches, involving customizing hardware accelerators for efficient LLM deployment. Finally, the paper examines LLM-aided design methodologies, focusing on High-Level Synthesis (HLS) functional verification, by creating a new dataset that contains a large number of buggy and bug-free codes. The authors propose novel solutions such as Medusa, a parallel decoding framework, and SnapKV, a method for reducing KV cache size, to enhance LLM efficiency and performance. They also discuss future research directions, including enhanced versatility in parallel decoding, combining KV compression with parallel decoding, and reconfigurable and heterogeneous hardware for LLMs. The paper concludes with a comprehensive overview of these advancements and future directions, aiming to pave the way for more efficient and scalable deployment of LLMs across diverse applications.