However, in many news stories I have read, I see a confusion as to what is being discussed.
I was once asked why I call it a "veil", when I really should be calling it a "headscarf". My answer was simple, I call it a veil because that's the regular term used, specifically on Muslim sites.
This article comes to give a simple explanation of the different types of veil and a run down of what's happening across Europe. I hope to keep it updated as things change.
The following pictures are taken from the BBC site, which brings an example of the different types of veil.
The hijab, which leaves the face uncovered.

The niqab which only leaves the eyes uncovered, and the burqa, which covers everything.

Belgium
Burqa banned in public.
France
The hijab is banned in public schools.
The burqa/niqab is banned in public.
Germany
On going debate.
Italy
North League proposes burqa ban.
Burqa banned in some cities.
Netherlands
Parliament pushes to ban the wearing of the burqa. PVV party wants referendum. Currently in discussions in the government.
Norway
Niqab banned in schools in Oslo
Spain
Several cities banned the burqa.
No national school headscarf policy.
Sweden
Gov't minister wants to ban hijab for girls under 15.
Niqab/Burka can be banned in schools. National Agency for Education affirms the right to wear a veil.
UK
Ongoing debate.
Last updated: Oct. 26, 2011