Now one of Scotland's largest power firms is offering a record £20,000 reward to help catch them in the act.
The organised gang are selling the cables to scrap dealers but this lucrative business is also extremely dangerous.
They target power lines in remote areas, in broad daylight, because it can take up to five hours to cut down the high-voltage lines.
One man has already died trying to steal copper from an electricity pole in Lanarkshire and others have suffered horrific burns, loss of limbs and scarring.
Scottish Power said about 20 power line thefts had been reported across central Scotland in just over two weeks.
These include incidents at Milngavie, Dalry, Shotts, Kilbarchan and Larkhall. In one incident, 1500 homes were without power.
Guy Jefferson, network operations director at Scottish Power Energy Networks, said: "Metal theft is one of the biggest threats to the safety of the electricity network, and the impact of these crimes can be devastating.
"One man died recently attempting to steal copper from an electricity pole in Lanarkshire, and others have suffered horrific burns, loss of limbs and scarring.
"In recent years we have witnessed house fires and damaged electrical appliances in homes."
Sources believe the gang responsible for the major power line thefts are operating out of Glasgow.
Scottish Power said there had been more than 850 metal thefts on its network since January 2011.
One incident last year, from a substation in Greenock, resulted in two serious house fires and more than 200 properties suffering a blackout.
In 2011, a botched cable theft in Glasgow triggered a 30-minute power outage for 50,000 properties in the South Side.
Mr Jefferson added: "We continue to increase our own security measures, and work closely with the police and other industries affected by this crime.
"I'd urge anyone who spots suspicious behaviour near our power lines to report what they have seen to the police."
Scottish Power has set up a hotline for the public to call with information, 0800 092 9290, or call the police on 101.