Campaigners from smokers' group Forest have criticised the ban as an example of "creeping prohibition".
Cities including New York, Toronto and Hong Kong have already banned smoking in key outdoor locations but Bristol is the UK's first to pilot smoke free zones.
Millennium and Anchor Squares are home to the At-Bristol science museum, shops and restaurants, and are well-used play spaces for children.
Two squares in Bristol will become the first major public outdoor spaces in UK to go smoke-free.
From today a voluntary smoking ban will be in place in Millennium Square and Anchor Square. The area is home to the At-Bristol science museum and often hosts festivals and other family friendly events.
The project is part of the Smokefree South West campaign.
Smoking isn't just bad for YOU - it can also make your children fatter. That's the conclusion from the latest Children of the 90s study.
The group based at Bristol University is following the health and development of more than 10,000 youngsters.
They've found that starting smoking at a young age can lead to problems for the next generation. Caron Bell reports.
A giant red ball is being pushed through Bristol today as part of a stop smoking campaign. Research shows that smoking is the biggest killer in the UK with half of long-term smokers dying prematurely from a smoking disease.
An ex-smoker will be running 28 miles around the city as part of the campaign Stoptober.
Our presenter Kylie Pentelow interviews Alison Birkett from Cancer Research UK about disturbing figures about children in our region taking up smoking.
A new study has revealed that almost 2,000 fewer patients are being admitted to hospital for emergency treatment for asthma since smokefree legislation was introduced in 2007.
Researchers based at Bath University found there was an immediate 4.9 per cent reduction in emergency hospital admissions for asthma in adults. It implies almost 1,900 admissions were prevented during the first year after legislation was introduced and a similar number in the subsequent two years.
People who smoke roll-ups are being targeted as part of a New Year campaign by Smokefree South West.
The campaign aims to dispel the myth that they are less harmful than manufactured cigarettes. More than 4,000 toxic chemicals are inhaled when smoking a roll up.