For many decades, the most popular tallit material, for those who found wool beyond their budget (or suffered from wool allergy) was a synthetic weave, commonly referred to as Acrylan. Acrylan tallits don't look as nice, don't drape well and are less durable. Still, they were the leading alternative to wool.
A few years ago a long-standing tallit maker named K'Nesher, based in Jerusalem, worked hard to develop a new alternative – a cotton tallit. Cotton not only looks much nicer than acrylan (and is even on a par with wool) but it also is superior from a halachic standpoint, since according to all opinions a cotton tallit can be used to fulfill the mitzvah of tzitzit (whereas acrylan is somewhat problematic).