The ageing population has grown quickly in the last half century with increased longevity and declining birth rate. This presents challenges to health services and the wider society. This review paper considers different aspects (e.g., physical, mental, and social well-being) of healthy ageing and how health devices can help people to monitor health conditions, treat diseases and promote social interactions. Existing technologies for addressing non-physical (e.g., Alzheimer’s, loneliness) and physical (e.g., stroke, bedsores, and fall) related challenges are presented together with the drivers and constraints of using e-textiles for these applications. E-textiles provide a platform that enables unobtrusive and ubiquitous deployment of sensors and actuators for healthy ageing applications. However, constraints remain on battery, integration, data accuracy, manufacturing, durability, ethics/privacy issues, and regulations. These challenges can only effectively be met by interdisciplinary teams sharing expertise and methods, and involving end users and other key stakeholders at an early stage in the research.