They are as secure as your password/keys are secure. So far, a web exploit was able to compromise the keys of people who were logged in with a master password. That web exploit has been fixed and all lost funds have been promised to be reimbursed. I haven't read if there have been any changes to the way the keys are stored locally after that incident, but I have some faith that it's been made more secure now.
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Ok, cool. Thanks!