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Cyberwarfare is the word used to define the most aggressive form of attack by a foe or rival over the internet. It largely applies to actions by states and involves denying internet services to communities or countries, or, at worst, destroying critical infrastructure or industrial facilities.
One other use of the term is to describe activity by a national army that might accompany its invasion of another country using conventional forces. Most major states would today be expected to use cyberwarfare to attack another country's computer infrastructure as part of an invasion or aggression.
Cyberwarfare tends to be distinguished from other forms of hostile cyber activity. Cybercrime involves activities like raiding bank accounts. Cyber espionage describes the stealing of secrets. Cyberwarfare tends to describe an assault that affects the national security of the state that is victimised.
There are a number of hard examples of cyberwarfare in action. The attack on Estonia's internet system in 2007 by the Russian state -or its proxies - is one example. 
In 2010, there was the deployment of the Stuxnet worm, widely believed to have been used by the US and Israel to attack computer-controlled centrifuges at a uranium enrichment facility in Iran which disrupted the country's nuclear programme.