Sleep is an essential physiological activity, accounting for about one-third of our lives, which significantly impacts our memory, mood, health, and children’s growth. Especially after the COVID-19 epidemic, sleep health issues have attracted more attention. In recent years, with the development of wearable electronic devices, there have been more and more studies, products, or solutions related to sleep monitoring. Many mature technologies, such as polysomnography, have been applied to clinical practice. However, it is urgent to develop wearable or non-contacting electronic devices suitable for household continuous sleep monitoring. This paper first introduces the basic knowledge of sleep and the significance of sleep monitoring. Then, according to the types of physiological signals monitored, this paper describes the research progress of bioelectrical signals, biomechanical signals, and biochemical signals used for sleep monitoring. However, it is not ideal to monitor the sleep quality for the whole night based on only one signal. Therefore, this paper reviews the research on multi-signal monitoring and introduces systematic sleep monitoring schemes. Finally, a conclusion and discussion of sleep monitoring are presented to propose potential future directions and prospects for sleep monitoring.