The rapid advances in high-speed and low-power computing, communication, and sensor technologies have propelled the growth of Internet-of-Things (IoT) technology. IoT enables sensors, actuators, and devices to work together in applications such as a smart home to track the health, activity, comfort, and well-being of residents, thus potentially revolutionizing the healthcare system. Textile-based wearables offer a promising solution to monitor health and activity in a smart home setting while ensuring comfort and unobtrusiveness. In fact, there has been a growing trend among researchers to develop textile-based sensors for measuring and monitoring vital signs, such as heart rate, body temperature, respiratory rate, biochemicals, humidity, and activities of daily living (ADLs). Researchers are also actively pursuing the development of electronic components, which are based on textiles, thus creating a new generation of wearable technology. Therefore, it is no wonder that the smart-textile market is expected to grow to over ${\$}$ 4 billion by 2030. However, factors such as cost-effectiveness, manufacturing scalability, device performance, environmental and safety concerns, and privacy issues may impede the market penetration of smart textiles. In this article, we present a comprehensive overview of the current state of research and development in the manufacturing of smart textiles and textile-based sensors with a focus on their application in monitoring and management of health in a smart home environment.