Non-24-h sleep-wake disorder (non-24) is a circadian rhythm disorder occurring in 55-70% of totally blind individuals (those lacking conscious light perception) in which the 24-h biological clock (central, hypothalamic, circadian pacemaker) is no longer synchronized, or entrained, to the 24-h day. Instead, the overt rhythms controlled by the biological clock gradually shift progressively earlier or later (free run) in accordance with the clock's near-24-h period, resulting in a recurrent pattern of daytime hypersomnolence and night-time insomnia. Orally administered melatonin and the melatonin agonist tasimelteon have been shown to entrain (synchronize) the circadian clock, resulting in improvements in night-time sleep and daytime alertness. We review the basic principles of circadian rhythms necessary to understand and treat non-24. The time of melatonin or tasimelteon administration must be considered carefully. For most individuals, those with circadian periods longer than 24 h, low-dose melatonin should be administered about 6 h before the desired bedtime, while in a minority, those with circadian periods shorter than 24 h (more commonly female individuals and African-Americans), melatonin should be administered at the desired wake time. Small doses (e.g., 0.5 mg of melatonin) that are not soporific would thus be preferable. Administration of melatonin or tasimelteon at bedtime will entrain individuals with non-24 but at an abnormally late time, resulting in continued problems with sleep and alertness. To date, tasimelteon has only been administered 1 h before the target bedtime in patients with non-24. Issues of cost, dose accuracy, and purity may figure into the decision of whether tasimelteon or melatonin is chosen to treat non-24. However, there are no head-to-head studies comparing efficacy, and studies to date show comparable rates of treatment success (entrainment).