Photoplethysmography (PPG) is a low-cost, non-invasive, and optical technique used to detect blood volume changes in the microvascular tissue bed, measured from the skin surface. It has traditionally been used in commercial medical devices for oxygen saturation, blood pressure monitoring, and cardiac activity for assessing peripheral vascular disease and autonomic function. There has been a growing interest to incorporate PPG sensors in daily life, capable of use in ambulatory settings. However, inferring cardiac information (e.g. heart rate) from PPG traces in such situations is extremely challenging, because of interferences caused by motion. Following the IEEE Signal Processing Cup in 2015, numerous methods have been proposed for estimating particularly the average heart rate using wrist-worn PPG during physical activity. Details on PPG technology, sensor development, and applications have been well documented in the literature. Hence, in this paper, we have presented a comprehensive review of state-of-the-art research on heart rate estimation from wrist-worn PPG signals. Our review also encompasses brief theoretical details about PPG sensing and other potential applications-biometric identification, disease diagnosis using wrist PPG. This paper will set a platform for future research on pervasive monitoring using wrist PPG.