There has been vast literature that studies Conversational Agents (CAs) in facilitating older adults' health. The vast and diverse studies warrants a comprehensive review that concludes the main findings and proposes research directions for future studies, while few literature review did it from human-computer interaction (HCI) perspective. In this study, we present a survey of existing studies on CAs for older adults' health. Through a systematic review of 72 papers, this work reviewed previously studied older adults' characteristics and analyzed participants' experiences and expectations of CAs for health. We found that (1) Past research has an increasing interest on chatbots and voice assistants and applied CA as multiple roles in older adults' health. (2) Older adults mainly showed low acceptance CAs for health due to various reasons, such as unstable effects, harm to independence, and privacy concerns. (3) Older adults expect CAs to be able to support multiple functions, to communicate using natural language, to be personalized, and to allow users full control. We also discuss the implications based on the findings.