Since the late 19th century, researchers have measured and predicted the acoustic properties of single-reed instruments like the clarinet and saxophone. According to musicians, the reed itself has a significant impact on sound production and playing comfort. However, the physics of the reed remains incompletely understood, and reed makers are constantly seeking a deeper comprehension that could allow them to deduce physical parameters that more adequately account for the sensations of musicians. This is the reason why some researchers are interested in studying the behavior of reeds, either through the creation of physical models or through physical or perceptual experiments. The present paper proposes a review of these studies, structured into three sections. Firstly, the physics of single-reeds and single-reed instruments is exposed and described by various models of increasing complexity. The experimental studies about single cane reeds are then detailed in the second and third sections, which respectively deal with perceptual assessments and physical measurements. Finally, the conclusion synthesizes and brings together the findings from each section to provide a comprehensive overview of current knowledge while also highlighting prospects for future research.