In the Old Souq at Deira and in traditional boutiques in malls you'll see colorful jalabiyas or women's kanduras, which are increasingly being bought by foreign women.
When out in public or in the company of men who aren't family, Emirati women wear the ubiquitous black cloak-like abaya and black shaylah wrapped around their head - tightly if devout, more loose if less conservative. The most religious women we're a Saudi-style niqab that ties around the head and covers all but the eyes. When worn with gloves and socks, so not an inch of skin is revealed, it's known as hijab.
Underneath the abaya and shaylah, young Emirati women wear designer fashions and jeans and t-shirts. However, when they're at home with family, along with older ladies, more traditional-minded women will wear a jallabiya or women's kandura.
Some of these are very simple, made from floral cotton prints, while others, like those in the photo above, are a lot more elegant, made from silks and linens, and decorated with applique, sequins, gems, tassles, and crocheted and embroidered features.
In the days before the discovery of oil, Emirati women didn't wear abayas and shaylahs. They wore these dresses in public with a gauzy face veil and baggy pantaloons. These days the pantaloons have been replaced with smart matching trousers.
Over the years, jalabiyas and kanduras have increasingly become a popular souvenir. If you're going to get one, make sure to buy some pretty sequined slippers to match!