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Despite these advancements in the past few years, LLMs have shown considerable vulnerabilities, particularly to prompt injection and jailbreaking attacks. This review analyzes the state of research on these vulnerabilities and presents available defense strategies. We roughly categorize attack approaches into prompt-based, model-based, multimodal, and multilingual, covering techniques such as adversarial prompting, backdoor injections, and cross-modality exploits. We also review various defense mechanisms, including prompt filtering, transformation, alignment techniques, multi-agent defenses, and self-regulation, evaluating their strengths and shortcomings. 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