Jailbreak attacks pose a serious threat to large language models (LLMs) by bypassing built-in safety mechanisms and leading to harmful outputs. Studying these attacks is crucial for identifying vulnerabilities and improving model security. This paper presents a systematic survey of jailbreak methods from the novel perspective of stealth. We find that existing attacks struggle to simultaneously achieve toxic stealth (concealing toxic content) and linguistic stealth (maintaining linguistic naturalness). Motivated by this, we propose StegoAttack, a fully stealthy jailbreak attack that uses steganography to hide the harmful query within benign, semantically coherent text. The attack then prompts the LLM to extract the hidden query and respond in an encrypted manner. This approach effectively hides malicious intent while preserving naturalness, allowing it to evade both built-in and external safety mechanisms. We evaluate StegoAttack on four safety-aligned LLMs from major providers, benchmarking against eight state-of-the-art methods. StegoAttack achieves an average attack success rate (ASR) of 92.00%, outperforming the strongest baseline by 11.0%. Its ASR drops by less than 1% even under external detection (e.g., Llama Guard). Moreover, it attains the optimal comprehensive scores on stealth detection metrics, demonstrating both high efficacy and exceptional stealth capabilities. The code is available at https://anonymous.4open.science/r/StegoAttack-Jail66