Large Language Models (LLMs), which bridge the gap between human language understanding and complex problem-solving, achieve state-of-the-art performance on several NLP tasks, particularly in few-shot and zero-shot settings. Despite the demonstrable efficacy of LLMs, due to constraints on computational resources, users have to engage with open-source language models or outsource the entire training process to third-party platforms. However, research has demonstrated that language models are susceptible to potential security vulnerabilities, particularly in backdoor attacks. Backdoor attacks are designed to introduce targeted vulnerabilities into language models by poisoning training samples or model weights, allowing attackers to manipulate model responses through malicious triggers. While existing surveys on backdoor attacks provide a comprehensive overview, they lack an in-depth examination of backdoor attacks specifically targeting LLMs. To bridge this gap and grasp the latest trends in the field, this paper presents a novel perspective on backdoor attacks for LLMs by focusing on fine-tuning methods. Specifically, we systematically classify backdoor attacks into three categories: full-parameter fine-tuning, parameter-efficient fine-tuning, and no fine-tuning. Based on insights from a substantial review, we also discuss crucial issues for future research on backdoor attacks, such as further exploring attack algorithms that do not require fine-tuning, or developing more covert attack algorithms.