The rapid increase in the number of older adults in developed countries has raised concerns about their well-being and increasing need for healthcare. New technologies, including Internet of Things, are being used to monitor older adults' health and activities, thus enabling them to live safely and independently at home as they age. However, Internet of Things monitoring solutions create privacy challenges that need to be addressed. This review examines how privacy has been conceptualised in studies proposing new Internet of Things solutions for monitoring older adults. The literature reviewed mostly links privacy with information security and unauthorised accessibility threats. There is a limited consideration of other aspects of privacy such as confidentiality and secondary use of users' information. We argue that developers of Internet of Things solutions that aim to monitor and collect health data about older adults need to adopt an expanded view of privacy. This will ensure that safeguards are built in to Internet of Things devices to protect and maintain users' privacy while also enabling the appropriate sharing of data to support older adults' safety and wellbeing.