Ensuring the security of large language models (LLMs) is an ongoing challenge despite their widespread popularity. Developers work to enhance LLMs security, but vulnerabilities persist, even in advanced versions like GPT-4. Attackers exploit these weaknesses, highlighting the need for proactive cybersecurity measures in AI model development. This article explores two attack categories: attacks on models themselves and attacks on model applications. The former requires expertise, access to model data, and significant implementation time, while the latter is more accessible to attackers and has seen increased attention. Our study reviews over 100 recent research works, providing an in-depth analysis of each attack type. We identify the latest attack methods and explore various approaches to carry them out. We thoroughly investigate mitigation techniques, assessing their effectiveness and limitations. Furthermore, we summarize future defenses against these attacks. We also examine real-world techniques, including reported and our implemented attacks on LLMs, to consolidate our findings. Our research highlights the urgency of addressing security concerns and aims to enhance the understanding of LLM attacks, contributing to robust defense development in this evolving domain.