Large Language Models (LLMs) are increasingly explored as a means to enhance smart home systems for elderly care, offering more natural interaction, contextual reasoning, and adaptive support compared to traditional rule-based approaches. Although prior work across artificial intelligence, human–computer interaction, and ambient assisted living has highlighted their potential, existing research remains scattered and lacks an integrated overview. To address this gap, we conducted a systematic review following PRISMA 2020 guidelines, examining a wide body of literature from January 2020 to October 2025, from which 17 featured papers are included after careful screening and assessment. The selected studies demonstrate LLM applications in natural language control, activity and health monitoring, safety and anomaly detection, and personalized assistance, employing models ranging from GPT-family systems to multimodal and domain-adapted architectures. Overall, the findings show strong capabilities in zero-shot understanding, contextual reasoning, and multi-turn dialogue, yet they also reveal notable challenges, including limited safety evaluation, privacy concerns, a lack of real-world deployment, and minimal engagement of older adults in system validation. This review synthesizes current progress and highlights key directions for advancing safe, reliable, and practical LLM-enabled smart home technologies to support aging in place.