Fall detection (FD) systems are crucial for identifying falls and ensuring timely assistance, thus reducing the risk of serious injuries. With the development of society and increasing attention to health issues, researchers have conducted extensive studies on falls to reduce the severe sequelae of falls. Integrating FD systems with the Internet of Things (IoT), particularly the Internet of Medical Things (IoMT), has significantly advanced healthcare and personal safety. This dynamic relationship between FD technology and IoT has opened up new vistas for monitoring and assisting individuals, particularly the elderly and those with health conditions that make them prone to falls. This article presents a review of wearable sensor-based FD techniques. We classify the detection methods into their categories from an algorithmic perspective: threshold-based, conventional machine learning-based, and deep learning-based methods. In addition, we identify and summarize the available data sets that can be used to evaluate the performance of the introduced methods. This review aims to provide researchers with a better comprehension of the FD problem, intending to foster further advancements in the field.