Wearable devices use sensors to evaluate physiological parameters, such as the heart rate, pulse rate, number of steps taken, body fat and diet. The continuous monitoring of physiological parameters offers a potential solution to assess personal healthcare. Identifying outliers or anomalies in heart rates and other features can help identify patterns that can play a significant role in understanding the underlying cause of disease states. Since anomalies are present within the vast amount of data generated by wearable device sensors, identifying anomalies requires accurate automated techniques. Given the clinical significance of anomalies and their impact on diagnosis and treatment, a wide range of detection methods have been proposed to detect anomalies. Much of what is reported herein is based on previously published literature. Clinical studies employing wearable devices are also increasing. In this article, we review the nature of the wearables-associated data and the downstream processing methods for detecting anomalies. In addition, we also review supervised and un-supervised techniques as well as semi-supervised methods that overcome the challenges of missing and un-annotated healthcare data.