The increased demand for well-being has fueled interest in sleep. Research in technology for monitoring sleep ranges from sleep efficiency and sleep stage analysis to sleep disorder detection, centering on wearable devices such as fitness bands, and some techniques have been commercialized and are available to consumers. Recently, as interest in digital therapeutics has increased, the field of sleep engineering demands a technology that helps people obtain quality sleep that goes beyond the level of monitoring. In particular, interest in sleep aids for people with or without insomnia but who cannot fall asleep easily at night is increasing. In this review, we discuss experiments that have tested the sleep-inducing effects of various auditory stimuli currently used for sleep-inducing purposes. The auditory stimulations were divided into (1) colored noises such as white noise and pink noise, (2) autonomous sensory meridian response sounds such as natural sounds such as rain and firewood burning, sounds of whispers, or rubbing various objects with a brush, and (3) classical music or a preferred type of music. For now, the current clinical method of receiving drugs or cognitive behavioral therapy to induce sleep is expected to dominate. However, it is anticipated that devices or applications with proven ability to induce sleep clinically will begin to appear outside the hospital environment in everyday life.