A few supplements have a real evidence base for sleep, and a great deal of marketing piled on top. The honest picture is that the better-supported ones tend to help at the edges, with onset or quality, rather than knock you out the way a sleeping pill would. None of them substitutes for the basics: a consistent wake time, a dark cool room, and getting off screens and caffeine earlier than feels necessary.
Magnesium
Magnesium, especially the glycinate form, is the most sensible starting point. It is mildly calming, the glycine it is bound to has a gentle role in sleep itself, and the safety margin is wide. The effect is modest rather than dramatic, but it is low-risk and a reasonable first thing to try, taken in the evening.
Glycine
Glycine, taken as a few grams before bed, has some genuine trial evidence for improving how quickly people fall asleep and how rested they feel the next day. It works partly by gently lowering core body temperature, which is part of how the body initiates sleep. It is cheap, well tolerated, and worth a try if magnesium alone is not enough.
Melatonin (a UK note)
Melatonin is worth understanding carefully. In the UK it is a prescription medicine, not an over-the-counter supplement as it is in the US. Its evidence is strongest for problems with timing: jet lag, shift work, and delayed sleep phase, where it helps shift the body clock. For ordinary "I can't switch off" insomnia its effect is smaller than its reputation suggests. It is best thought of as a body-clock tool rather than a sedative.
L-theanine
L-theanine, the calming compound in tea, can take the edge off a racing mind in the evening. The sleep evidence is lighter than for magnesium or glycine, but it is very safe and some people find it helpful for winding down rather than for sleep itself.
The honest version
Start with the basics and magnesium, add glycine if you need more, treat melatonin as a timing tool, and keep expectations realistic about the rest. If your sleep problem is really a stress problem in disguise, that may be the better place to start. To check any sleep supplement against a medication you take, the free checker will show you the result and the reasoning.