The most crucial comprises of dart is the barrel. This is the part of the dart you grip when you throw and it also gives the dart its weight. The shape of the barrel will vary depending on where the weight is concentrated.
Tungsten is a very dense metal, also very durable. Using tungsten to make a dart barrel results in a smaller dart for the same weight. For anyone who plays darts often, the durability is important, as that helps retain the dart's precision-machined shape, grooves, and knurling.
Today's standard material of tungsten barrel is tungsten heavy alloy barrel. Tungsten is a very dense material, so darts with a considerable weight can be made quite slim. The invention of tungsten heavy alloy barrels had a big impact on the sport. With the new darts it was possible to achieve much better grouping than before, and the averages in pro games have improved dramatically. It is not an overstatement when this development is referred to as "the tungsten revolution".
Remember: the only benefit from a high tungsten share is that the dart can be made slimmer than a dart with the same weight and a lower tungsten share. In no way do higher tungsten percentages indicate some sort of overall better quality or better machining.
In recent years a growing number of people has become allergic to Nickel. With Nickel-Tungsten darts being the standard equipment nowadays these people will have problems with their darts. There are a few darts available with different tungsten alloys, such as silver tungsten or copper tungsten. However, these darts are very rare. The major dart manufacturers don't supply them. If you are allergic to Nickel you will probably have to look for these alternatives.
Because of technical difficulties with manufacturing a 100% tungsten dart barrel is not available. All "tungsten" darts you can buy are in fact made of tungsten heavy alloy, with Nickel-Iron-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, Copper and/or Ferro. Tungsten darts are available from 80% to over 90%. The more tungsten the slimmer - and the more expensive - the dart is. If the high-percentage tungsten darts are worth the higher price is an open question. Personally I think that 80% tungsten are good enough for almost everyone.