Heart rate is a crucial indicator of human health with significant physiological importance. Traditional contact methods for measuring heart rate, such as electrocardiograph or wristbands, may not always meet the need for convenient health monitoring. Remote photoplethysmography (rPPG) provides a non-contact method for measuring heart rate and other physiological indicators by analyzing blood volume pulse signals. This approach is non-invasive, does not require direct contact, and allows for long-term healthcare monitoring. Deep learning has emerged as a powerful tool for processing complex image and video data, and has been increasingly employed to extract heart rate signals remotely. This article reviewed the latest research advancements in rPPG-based heart rate measurement using deep learning, summarized available public datasets, and explored future research directions and potential advancements in non-contact heart rate measurement.