Large Language Models (LLMs) have transformed artificial intelligence by advancing natural language understanding and generation, enabling applications across fields beyond healthcare, software engineering, and conversational systems. 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. We also discuss key metrics and benchmarks used to assess LLM safety and robustness, noting challenges like the quantification of attack success in interactive contexts and biases in existing datasets. Identifying current research gaps, we suggest future directions for resilient alignment strategies, advanced defenses against evolving attacks, automation of jailbreak detection, and consideration of ethical and societal impacts. This review emphasizes the need for continued research and cooperation within the AI community to enhance LLM security and ensure their safe deployment.