At present the assembly can pass legislation in 20 devolved policy areas, including health and education.
A Yes vote would mean it no longer needs to apply to parliament for law-making powers on a case-by-case basis.
Voting is until 2200 GMT. The count starts on Friday morning, with a final result likely in the afternoon.
A No vote would keep the existing system, while a Yes would mean the assembly can pass laws without first seeking consent in Westminster.
However, if there was a Yes the assembly would not gain powers over new areas.
Thursday, 3 March 2011
Fun voting times (by Lotte)
Today I did some social change by posting a random-act-of-kindness to a woman who runs a kids' knitting group, which was satisfying. I also VOTED. And if you're in Wales, you should too. Polls close at 10pm, and even if you don't have your polling card your name will still be on the list.
Here's my satisfyingly gloominous and gothic polling station entrance for your perusal.
The haps are, and I thieve shamelessly from the BBC: