Before the tungsten revolution, darts were mainly made of copper, steel or brass. Brass darts are still used by some players because they are much cheaper than Tungsten's. But brass darts are ancient technology now, so they are not used by the most professional dart players.
Today's standard material is Nickel-Tungsten. Tungsten is a very dense material, so darts with a considerable weight can be made quite slim. Because of technical difficulties with manufacturing 100% tungsten darts are not available. All "tungsten"darts are in fact made of tungsten alloys, with Nickel-Tungsten being the most common one. When you buy a dart the amount of tungsten in the alloy is given by a percentage number. So a common "80% Tungsten" dart has 80 percent tungsten and 20 percent Nickel. Tungsten darts are available from 80% to over 90%. The more tungsten the slimmer and the more expensive generall, the darts will be.