The big question I keep hearing is; I'm in the US (or other non-EU country), does GDPR apply to my company or organization?
The shortest possible answer is: Maybe :)
The answer is: YES if your company has a physical or legal presence (like an office, employee, parent-company, subsidiary, etc.) in an EU country. The GDPR applies to you and you need to to start reading up ASAP as you only have a few weeks to figure this all out.
The answer is likley: NO (but be careful here) if you have no physical or legal presence in the EU. Bonus points if your business isn't really aimed at the EU.
The answer is likley still: NO if again, you have no physical or legal presence in the EU but do rely on EU traffic as a direct or significant part of your business. At that point is all about how much risk you're willing to take on as we see how this law is interpreted.
Any country can claim this over any other territory they wish. But that doesn't make it true. For the claim to be effective (except by use of force), it must be agreed either with the legal authority of the country.
Right now there appears to be none. No one is clearly citing any treaty with the EU as giving them this authority.
Disclaimer: This isn't legal advice. This is my personal view
on a complicated issue that I'm trying to discuss in order
to learn more myself.