It's happening on both sides of the Atlantic.
Just last week, we reported that the US Federal Trade Commission (FTC) has issued a warning explaining how phishing gangs are using the turmoil in the financial world to extract valuable information from consumers.
Meanwhile, in the UK, a UK banking group has revealed that phishing attacks were up more than 180% in a year.
And now, the FBI's cyber division head has said that computer spying and theft of personal information is rising sharply.
FBI Assistant Director Shawn Henry told reporters: "Over the past year the malicious activity has become much more prevalent. The threat continues to increase".
In particular, but without naming the countries, Henry said that as many as 24 countries have taken an "aggressive interest" in penetrating the networks of US companies and government agencies.
Online reports suggest China and Russia may be amongst the countries the FBI is watching.
The Internet Crime Complaint Center, which the FBI part runs, has recorded more than one million complaints since its founding in 2000, but Henry admitted that numbers are now running about 18,000 to 20,000 per month.