Giant Squid & Octopus: History and Evidence

Tales of giant squids and octopuses have cropped up many times in the legends of many places... but what's real and not?

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It seems likely there have never been any such animals big enough to drag a boat under water, as some tales tell; but exactly how big can either species actually get? Below are known claims for evidence of giant squids and octopuses, as well as a bit of history of their trip from legend to scientifically recognized animals.